Deck 14: Inference About Simple Regression

Question 1

Which expression is a regression equation for a simple linear relationship in a population?

A) $\hat{y}$ = b₀ + b₁ x
B) $\hat{y}$ = 44 + 0.60 x
C)
D)

Answer 1

Question 2

The slope of the regression line tells us

A) the average value of x when y = 0.
B) the average value of y when x = 0.
C) how much the average value of y changes per one unit change in x.
D) how much the average value of x changes per one unit change in y.

Answer 2

how much the average value of y changes per one unit change in x.

Question 3

A regression line is used for all of the following except one. Which one is not a valid use of a regression line?

A) to estimate the average value of y at a specified value of x.
B) to predict the value of y for an individual, given that individual's x-value.
C) to estimate the change in y for a one-unit change in x.
D) to determine if a change in x causes a change in y.

Answer 3

to determine if a change in x causes a change in y.

Question 4

Which statement is not one of the assumptions made about a simple linear regression model for a population?

A) The variance of Y is the same for every value of x.
B) The distribution of Y follows a normal distribution at every value of x.
C) The average (or mean) of Y changes linearly with x.
D) The deviations (or residuals) follow a normal distribution with mean .

Question 5

Which choice is not an appropriate description of $\hat{y}$ in a regression equation?

A) Estimated response
B) Predicted response
C) Estimated average response
D) Observed response

Question 6

Which choice is not an appropriate term for the x variable in a regression equation?

A) independent variable
B) dependent variable
C) predictor variable
D) explanatory variable

Question 7

What is the best way to determine whether or not there is a statistically significant linear relationship between two quantitative variables?

A) Compute a regression line from a sample and see if the sample slope is 0.
B) Compute the correlation coefficient and see if it is greater than 0.5 or less than -0.5.
C) Conduct a test of the null hypothesis that the population slope is 0.
D) Conduct a test of the null hypothesis that the population intercept is 0.

Question 8

In a statistics class at Penn State University, a group working on a project recorded the time it took each of 20 students to drink a 12-ounce beverage and also recorded body weights for the students. Which of these statistical techniques would be the most appropriate for determining if there is a statistically significant relationship between drinking time and body weight? (Assume that the necessary conditions for the correct procedure are met.)

A) Compute a chi-square statistic and test to see if the two variables are independent.
B) Compute a regression line and test to see if the slope is significantly different from 0.
C) Compute a regression line and test to see if the slope is significantly different from 1.
D) Conduct a paired difference t-test to see if the mean difference is significantly different from 0.

Question 9

To determine if there is a statistically significant relationship between two quantitative variables, one test that can be conducted is

A) a t-test of the null hypotheses that the slope of the regression line is zero.
B) a t-test of the null hypotheses that the intercept of the regression line is zero.
C) a test that the correlation coefficient is less than one.
D) a test that the correlation coefficient is greater than one.

Question 10

The r² value is reported by a researcher to be 49%. Which of the following statements is correct?

A) The explanatory variable explains 49% of the variability in the response variable.
B) The explanatory variable explains 70% of the variability in the response variable.
C) The response variable explains 49% of the variability in the explanatory variable.
D) The response variable explains 70% of the variability in the explanatory variable.

Question 11

Shown below is a scatterplot of y versus x. Which choice is most likely to be the approximate value of r², the proportion of variation in y explained by the linear relationship with x?

A) 0%
B) 5%
C) 63%
D) 95%

Question 12

Shown below is a scatterplot of y versus x. Which choice is most likely to be the approximate value of r², the proportion of variation in y explained by the linear relationship with x?

A) 0%
B) 63%
C) 95%
D) 99%

Question 13

Shown below is a scatterplot of y versus x.
Which choice is most likely to be the approximate value of r², the proportion of variation in y explained by the linear relationship with x?

A) -99.5%
B) 2.0%
C) 50.0%
D) 99.5%

Question 14

Use the following information for questions:
A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is:
Temperature = 110 - 2(Latitude).

-Estimate the average January temperature for a city at Latitude = 45.

A) 10 degrees
B) 20 degrees
C) 30 degrees
D) 45 degrees

Question 15

Use the following information for questions:
A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is:
Temperature = 110 - 2(Latitude).

-How does the estimated temperature change when latitude is increased by one?

A) It goes up 2 degrees.
B) It goes up 108 degrees.
C) It goes up 110 degrees.
D) It goes down 2 degrees.

Question 16

Use the following information for questions:
A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is:
Temperature = 110 - 2(Latitude).

-Based on the equation, what can be said about the association between temperature and latitude in the sample?

A) There is a positive association.
B) There is no association.
C) There is a negative association.
D) The direction of the association can't be determined from the equation.

Question 17

Use the following information for questions:
A regression equation is determined that describes the relationship between average January temperature (degrees Fahrenheit) and geographic latitude, based on a random sample of cities in the United States. The equation is:
Temperature = 110 - 2(Latitude).

-Suppose that the latitudes of two cities differ by 10. What is the estimated difference in the average January temperatures in the two cities?

A) 2 degrees
B) 10 degrees
C) 20 degrees
D) 90 degrees

Question 18

Use the following information for questions:
Based on a representative sample of college men, a regression line relating y = ideal weight tox = actual weight, for men, is given by
Ideal weight = 53 + 0.7 *actual weight

-For a man with actual weight = 200 pounds, his ideal weight is predicted to be

A) 153 pounds.
B) 193 pounds.
C) 200 pounds.
D) 253 pounds.

Question 19

Use the following information for questions:
Based on a representative sample of college men, a regression line relating y = ideal weight tox = actual weight, for men, is given by
Ideal weight = 53 + 0.7 *actual weight

-If a man weighs 200 pounds but his ideal weight is 210 pounds, then his residual is

A) 10 pounds.
B) -10 pounds.
C) 17 pounds.
D)-17 pounds.

Question 20

Use the following information for questions:
Based on a representative sample of college men, a regression line relating y = ideal weight tox = actual weight, for men, is given by
Ideal weight = 53 + 0.7 *actual weight

-In this situation, if a man has a residual of 10 pounds it means that

A) his predicted ideal weight is 10 pounds more than his stated ideal weight.
B) his predicted ideal weight is 10 pounds less than his stated ideal weight.
C) his predicted ideal weight is 10 pounds more than his actual weight.
D) his predicted ideal weight is 10 pounds less than his actual weight.

Question 21

Use the following information for questions:
Based on a representative sample of college men, a regression line relating y = ideal weight tox = actual weight, for men, is given by
Ideal weight = 53 + 0.7 *actual weight

-In this context, the slope of +0.7 indicates that

A) all men would like to weigh 0.7 pounds more than they do.
B) on average, men would like to weigh 0.7 pounds more than they do.
C) on average, as ideal weight increases by 1 pound actual weight increases by 0.7 pounds.
D) on average, as actual weight increases by 1 pound ideal weight increases by 0.7 pounds.

Question 22

Use the following information for questions:
The relation between y = ideal weight (lbs) and x =actual weight (lbs), based on data fromn = 119 women, resulted in the regression line $\hat{y}$ = 44 + 0.60 x

-The slope of the regression line is ______

A) 119
B) 44
C) 0.60
D) None of the above

Question 23

Use the following information for questions:
The relation between y = ideal weight (lbs) and x =actual weight (lbs), based on data fromn = 119 women, resulted in the regression line $\hat{y}$ = 44 + 0.60 x

-The intercept of the regression line is ______

A) 119
B) 44
C) 0.60
D) None of the above

Question 24

Use the following information for questions:
The relation between y = ideal weight (lbs) and x =actual weight (lbs), based on data fromn = 119 women, resulted in the regression line $\hat{y}$ = 44 + 0.60 x

-The estimated ideal weight for a women who weighs 118 pounds is ______

A) 120.0 pounds.
B) 118.0 pounds.
C) 114.8 pounds.
D) None of the above

Question 25

Use the following information for questions:
The relation between y = ideal weight (lbs) and x =actual weight (lbs), based on data fromn = 119 women, resulted in the regression line $\hat{y}$ = 44 + 0.60 x

-What is the interpretation of the value 0.60 in the regression equation for this question?

A) The proportion of women whose ideal weight is greater than their actual weight.
B) The estimated increase in average actual weight for an increase on one pound in ideal weight.
C) The estimated increase in average ideal weight for an increase of one pound in actual weight.
D) None of the above

Question 26

Use the following information for questions:
The relation between y = ideal weight (lbs) and x =actual weight (lbs), based on data fromn = 119 women, resulted in the regression line $\hat{y}$ = 44 + 0.60 x

-What is the interpretation of the value 44 in the regression for this question?

A) The slope of the regression line.
B) The difference between the actual and ideal weight for a woman who weighs 100 pounds.
C) The ideal weight for a woman who weighs 0 pounds.
D) None of the above

Question 27

Use the following information for questions:
The relation between y = ideal weight (lbs) and x =actual weight (lbs), based on data fromn = 119 women, resulted in the regression line $\hat{y}$ = 44 + 0.60 x

-If a woman weighs 100 pounds and her ideal weight is just that, 100 pounds, then her residual is

A)-4 pounds
B) 4 pounds
C) 44 pounds
D) None of the above

Question 28

Use the following information for questions:
The relation between y = ideal weight (lbs) and x =actual weight (lbs), based on data fromn = 119 women, resulted in the regression line $\hat{y}$ = 44 + 0.60 x

-If a woman weighs 120 pounds and her ideal weight is just that, 120 pounds, then her residual is

A)-4 pounds
B) 4 pounds
C) 44 pounds
D) None of the above

Question 29

Use the following information for questions:
A representative sample of 190 students resulted in a regression equation between y = left hand spans (cm) and x = right hand spans (cm). The least squares regression equation is $\hat{y}$ = 1.46 + 0.938 x. The error sum of squares (SSE) was 76.67, and total sum of squares (SSTO) was 784.8.

-What is the estimated standard deviation for the regression, s?

A) 0.6352
B) 0.6369
C) 0.6386
D) None of the above

Question 30

Use the following information for questions:
A representative sample of 190 students resulted in a regression equation between y = left hand spans (cm) and x = right hand spans (cm). The least squares regression equation is $\hat{y}$ = 1.46 + 0.938 x. The error sum of squares (SSE) was 76.67, and total sum of squares (SSTO) was 784.8.

-For a student with a right hand span of 26 cm, what is the estimated left hand span?

A) 24.39
B) 25.85
C) 29.60
D) None of the above

Question 31

Use the following information for questions:
A representative sample of 190 students resulted in a regression equation between y = left hand spans (cm) and x = right hand spans (cm). The least squares regression equation is $\hat{y}$ = 1.46 + 0.938 x. The error sum of squares (SSE) was 76.67, and total sum of squares (SSTO) was 784.8.

-For a student with a right and left hand span of 26 cm, what is the value of the residual?

A) -0.152
B) 0.152
C) 25.848
D) 26

Question 32

Use the following information for questions:
A representative sample of 190 students resulted in a regression equation between y = left hand spans (cm) and x = right hand spans (cm). The least squares regression equation is $\hat{y}$ = 1.46 + 0.938 x. The error sum of squares (SSE) was 76.67, and total sum of squares (SSTO) was 784.8.

-Use the empirical rule to find an interval that describes the left hand spans of approximately 95% of all individuals who have a right hand span of 26 cm.

A) (23.12, 25.66)
B) (24.57, 27.12)
C) (28.33, 30.87)
D) None of the above

Question 33

Use the following information for questions:
A representative sample of 190 students resulted in a regression equation between y = left hand spans (cm) and x = right hand spans (cm). The least squares regression equation is $\hat{y}$ = 1.46 + 0.938 x. The error sum of squares (SSE) was 76.67, and total sum of squares (SSTO) was 784.8.

-What is the value of r², the proportion of variation in left hand spans explained by the linear relationship with right hand spans.

A) 9.8%
B) 90.2%
C) 95.0%
D) None of the above

Question 34

Use the following information for questions:
The data from a representative sample of 43 male college students was used to determine a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation was $\hat{y}$ = -318 + 7.00 x. The error sum of squares (SSE) was 23617; the total sum of squares (SSTO) = 34894.

-What is the estimated standard deviation for the regression, s?

A) 24.0
B) 23.7
C) 23.4
D) None of the above

Question 35

Use the following information for questions:
The data from a representative sample of 43 male college students was used to determine a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation was $\hat{y}$ = -318 + 7.00 x. The error sum of squares (SSE) was 23617; the total sum of squares (SSTO) = 34894.

-For a male student with a height of 70 inches, what is the estimated weight?

A) 165
B) 170
C) 172
D) None of the above

Question 36

Use the following information for questions:
The data from a representative sample of 43 male college students was used to determine a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation was $\hat{y}$ = -318 + 7.00 x. The error sum of squares (SSE) was 23617; the total sum of squares (SSTO) = 34894.

-For a male student with a height of 70 inches and a weight of 200 lbs, what is the value of the residual?

A) -28
B) 28
C) 172
D) 200

Question 37

Use the following information for questions:
The data from a representative sample of 43 male college students was used to determine a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation was $\hat{y}$ = -318 + 7.00 x. The error sum of squares (SSE) was 23617; the total sum of squares (SSTO) = 34894.

-Use the empirical rule to find an interval that describes the weights of approximately 95% of male college students who are 70 inches tall.

A) (122.6, 217.4)
B) (118.2, 211.8)
C) (124, 220)
D) None of the above

Question 38

Use the following information for questions:
The data from a representative sample of 43 male college students was used to determine a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation was $\hat{y}$ = -318 + 7.00 x. The error sum of squares (SSE) was 23617; the total sum of squares (SSTO) = 34894.

-What is the proportion of variation in weight that is explained by the linear relationship with height?

A) 32.3%
B) 56.9%
C) 67.7%
D) None of the above

Question 39

Use the following information for questions:
Data from a sample of 10 student is used to find a regression equation relating y = score on a 100-point exam to x = score on a 10-point quiz. The least squares regression equation is $\hat{y}$ = 35 + 6 x. The standard error of the slope is 2. The following hypotheses are tested:
H₀: $?_1=0$
H_a: $?_1?0$

-What is the value of the t-statistic for testing the hypotheses?

A) -2.0
B) 2.0
C) 3.0
D) 0

Question 40

Use the following information for questions:
Data from a sample of 10 student is used to find a regression equation relating y = score on a 100-point exam to x = score on a 10-point quiz. The least squares regression equation is $\hat{y}$ = 35 + 6 x. The standard error of the slope is 2. The following hypotheses are tested:
H₀: $?_1=0$
H_a: $?_1?0$

-What is the p-value for the test? (Table A.3 or its equivalent needed.)

A) 0.009
B) 0.018
C) 0.080
D) None of the above

Question 41

Use the following information for questions:
Data from a sample of 10 student is used to find a regression equation relating y = score on a 100-point exam to x = score on a 10-point quiz. The least squares regression equation is $\hat{y}$ = 35 + 6 x. The standard error of the slope is 2. The following hypotheses are tested:
H₀: $?_1=0$
H_a: $?_1?0$

-What is a 95% confidence interval for $\beta$ ₁ ? (Table A.2 or its equivalent needed.)

A) (1.38, 10.62)
B) (1.48, 10.52)
C) (1.54, 10.46)
D) None of the above

Question 42

Use the following information for questions:
Data from a sample of 10 student is used to find a regression equation relating y = score on a 100-point exam to x = score on a 10-point quiz. The least squares regression equation is $\hat{y}$ = 35 + 6 x. The standard error of the slope is 2. The following hypotheses are tested:
H₀: $?_1=0$
H_a: $?_1?0$

-What is a 90% confidence interval for $\beta$ ₁? (Table A.2 or its equivalent needed.)

A) (2.08, 9.92)
B) (2.28, 9.72)
C) (2.34, 9.66)
D) None of the above

Question 43

Use the following information for questions:
A representative sample of n = 12 male college students is used to find a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation is $\hat{y}$ = 30 + 2 x. The standard error of the estimated slope is 1. The following hypotheses will be tested:
H₀: $?_1 = 0$
H_a: $?_1 ? 0$

-What is the value of the t-statistic for testing these hypotheses?

A) 1.0
B) 1.5
C) 2.0
D) 30

Question 44

Use the following information for questions:
A representative sample of n = 12 male college students is used to find a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation is $\hat{y}$ = 30 + 2 x. The standard error of the estimated slope is 1. The following hypotheses will be tested:
H₀: $?_1 = 0$
H_a: $?_1 ? 0$

-What is the p-value for the test? (Table A.3 or its equivalent needed.)

A) 0.074
B) 0.162
C) 0.226
D) None of the above

Question 45

Use the following information for questions:
A representative sample of n = 12 male college students is used to find a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation is $\hat{y}$ = 30 + 2 x. The standard error of the estimated slope is 1. The following hypotheses will be tested:
H₀: $?_1 = 0$
H_a: $?_1 ? 0$

-What is a 90% confidence interval for $\beta$ ₁? (Table A.2 or its equivalent needed.)

A) (0.35, 6.65)
B) (-1.32, 5.32)
C) (0.19, 3.81)
D) (0.00, 4.00)

Question 46

Use the following information for questions:
A representative sample of n = 12 male college students is used to find a regression equation for y = weight (lbs) and x = height (inches). The least squares regression equation is $\hat{y}$ = 30 + 2 x. The standard error of the estimated slope is 1. The following hypotheses will be tested:
H₀: $?_1 = 0$
H_a: $?_1 ? 0$

-What is the p-value for testing the following hypothesis about the correlation coefficient

A) 0.074
B) 0.162
C) 0.226
D) None of the above

Question 47

Use the following information for questions:
Grades for a random sample of students who have taken statistics from a certain professor over the past 20 year were used to estimate the relationship between y = grade on the final exam and x = average exam score (for the three exams given during the term).

-The results for a test of H₀: $\beta$ ₁ = 0 versus H_a $\beta$ ₁ $\neq$ 0 show that

A) the null hypothesis can be rejected because t = 3.91 and the p-value = 0.000.
B) the null hypothesis can be rejected because t = 14.01 and the p-value = 0.000.
C) the null hypothesis cannot be rejected because t = 3.91 and the p-value = 0.000.
D) the null hypothesis cannot be rejected because t = 14.01 and the p-value = 0.000.

Question 48

Use the following information for questions:
Grades for a random sample of students who have taken statistics from a certain professor over the past 20 year were used to estimate the relationship between y = grade on the final exam and x = average exam score (for the three exams given during the term).

-The estimate of the population standard deviation $\sigma$ is given by

A) SSE = 17097
B) MSE = 96
C) StDev = 4.246
D) S = 9.801

Question 49

Use the following information for questions:
Grades for a random sample of students who have taken statistics from a certain professor over the past 20 year were used to estimate the relationship between y = grade on the final exam and x = average exam score (for the three exams given during the term).

-The "Fit"information shown at the end of the output is for ExamAvg = 75. From this, we can conclude that

A) the probability is about 0.95 that a randomly selected student with an exam average of 75 will score between 74 and 77 on the final exam.
B) the final exam score for a randomly selected student with an exam average of 75 is likely to be between 56 and 95.
C) about 95% of the students with an exam average of 75 will score between 74 and 77 on the final exam.
D) the average final exam score for students with an exam average of 75 is likely to be between 56 and 95.

Question 50

Use the following information for questions:
Grades for a random sample of students who have taken statistics from a certain professor over the past 20 year were used to estimate the relationship between y = grade on the final exam and x = average exam score (for the three exams given during the term).

-The two values used to determine r² are

A) 17097 and 35952
B) 96 and 17097
C) 1 and 178
D) 178 and 179

Question 51

For the regression line $\hat{y}$ = b₀ + b₁ x, explain what the values b₀ and b₁ represent.

Question 52

Use the following information for questions:
A regression line relating y =student's height (inches) to x = father's height (inches) for n = 70 college males is $\hat{y}$ = 15 + 0.8 x.
-What is the estimated height of a son whose father's height is 70 inches?

Question 53

Use the following information for questions:
A regression line relating y =student's height (inches) to x = father's height (inches) for n = 70 college males is $\hat{y}$ = 15 + 0.8 x.
-If the son's actual height is 68 inches, what is the value of the residual?

Question 54

Use the following information for questions:
A linear regression analysis of the relationship between y = daily hours of TV watched andx = age is done using data from n = 50 adults. The error sum of squares is SSE = 1,000. The total sum of squares is SSTO = 5,000.
-What is the estimated standard deviation of the regression, s?

Question 55

Use the following information for questions:
A linear regression analysis of the relationship between y = daily hours of TV watched andx = age is done using data from n = 50 adults. The error sum of squares is SSE = 1,000. The total sum of squares is SSTO = 5,000.
-What is the value of r², the proportion of variation in daily hours of TV watching explained by the linear relationship with x = age?

Question 56

Use the following information for questions:
A linear regression analysis of the relationship between y = grade point average and x = hours studied per week is done using data from n = 10 students. The error sum of squares is SSE = 100 and the total sum of squares is SSTO = 900.
-What is the value of s = estimated standard deviation for the regression?

Question 57

Use the following information for questions:
A linear regression analysis of the relationship between y = grade point average and x = hours studied per week is done using data from n = 10 students. The error sum of squares is SSE = 100 and the total sum of squares is SSTO = 900.
-What is the value of r², the proportion of variation in grade point average explained by the linear relationship with x = hours studied per week?

Question 58

Use the following information for questions:
A regression line relating y = hours of sleep the previous day to x =hours studied the previous day is estimated using data from n = 10 students. The estimated slope b₁ = -0.30. The standard error of the slope is s.e.(b₁) = 0.20.

-What is the value of the test statistic for the following hypothesis test about $?_1$ , the population slope?
H₀: $?_1 = 0$
H_a: $?_1 ? 0$

Question 59

Use the following information for questions:
A regression line relating y = hours of sleep the previous day to x =hours studied the previous day is estimated using data from n = 10 students. The estimated slope b₁ = -0.30. The standard error of the slope is s.e.(b₁) = 0.20.

-What is the value of the p-value for the test in question 59?

Question 60

Use the following information for questions:
A regression line relating y = hours of sleep the previous day to x =hours studied the previous day is estimated using data from n = 10 students. The estimated slope b₁ = -0.30. The standard error of the slope is s.e.(b₁) = 0.20.

-What is a 90% confidence interval for $\beta$ ₁ , the population slope?

Question 61

Use the following information for questions:
A regression line relating y =grade point average to x = hours studied per week is estimated using data for n = 5 students. The estimated slope is b₁ = 0.02. The standard error of the slope is s.e.(b₁) = 0.01.
-What is the value of the test statistic for the following hypothesis test about $β_1$ , the population slope?
H₀: $β_1 = 0$
H_a: $β_1 ≠ 0$

Question 62

Use the following information for questions:
A regression line relating y =grade point average to x = hours studied per week is estimated using data for n = 5 students. The estimated slope is b₁ = 0.02. The standard error of the slope is s.e.(b₁) = 0.01.
-What is the value of the p-value for the test in question 62?

Question 63

Use the following information for questions:
A regression line relating y =grade point average to x = hours studied per week is estimated using data for n = 5 students. The estimated slope is b₁ = 0.02. The standard error of the slope is s.e.(b₁) = 0.01.

-What is a 95% confidence interval for $\beta$ ₁ , the population slope ?

Question 64

Use the following information for questions:
Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size.
-Identify the response and the explanatory variable.

Question 65

Use the following information for questions:
Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size.
-Consider the scatterplot below.
Does a linear relationship between price and size seem reasonable? If so, what appears to be the direction of the relationship?

Question 66

Use the following information for questions:
Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size.

-Some of the regression output is provided below.

Give the value of $r^2$ and interpret it in the context of the problem.

Question 67

Use the following information for questions:
Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size.
-Give the least square regression equation for predicting price from house size.

Question 68

Use the following information for questions:
Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size.
-What is the estimated change in the average selling price of a house for an increase in house size of 100 square feet?

Question 69

Use the following information for questions:
Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size.
-Predict the price for the 60^th observed house, which had a home size of 2430 square feet.

Question 70

Use the following information for questions:
Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size.
-The observed selling price for that house was $200,000. Compute the residual value.

Question 71

Use the following information for questions:
Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size.
-Write the null and alternative hypotheses for assessing if there is a significant positive linear relationship between price and size for the population of all houses in your town.

Question 72

Use the following information for questions:
Data has been obtained on the house size (in square feet) and the selling price (in dollars) for a sample of 100 homes in your town. Your friend is saving to buy a house and she asks you to investigate the relationship between house size and selling price and to develop a model to predict the price from size.
-Report the corresponding p-value and state the conclusion in context of this problem.

Question 73

What is the main distinction between a confidence interval and a prediction interval?

A) A confidence interval estimates the mean value of y at a particular value of x, while a prediction interval estimates the range of y values at a particular value of x.
B) A prediction interval estimates the mean value of y at a particular value of x, while a confidence interval estimates the range of y values at a particular value of x.
C) A confidence interval and a prediction interval are the same thing; they both estimate the mean value of y at a particular value of x.
D) A confidence interval and a prediction interval are the same thing; they both estimate the range of y values at a particular value of x.

Question 74

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A sample of 19 female bears was measured for chest girth (y) and neck girth (x), both in inches. The least squares regression equation relating the two variables is $\hat{y}$ = 5.32 + 1.53 x. The standard deviation of the regression is s = 3.692.

-What is a 95% confidence interval for the average (or mean) chest girth for bears with a neck girth of 20 inches? The standard error of the fit is s.e.(fit) = 0.880

A) (27.9, 43.9)
B) (28.1, 43.7)
C) (34.1, 37.8)
D) None of the above

Question 75

Use the following information for questions:
A sample of 19 female bears was measured for chest girth (y) and neck girth (x), both in inches. The least squares regression equation relating the two variables is $\hat{y}$ = 5.32 + 1.53 x. The standard deviation of the regression is s = 3.692.

-What is a 95% prediction interval for the chest girth of a bear with a neck girth of 20 inches? The standard error of the fit, s.e.(fit), = 0.880

A) (27.9, 43.9)
B) (28.1, 43.7)
C) (34.1, 37.8)
D) None of the above

Question 76

Use the following information for questions:
A sample of 19 female bears was measured for chest girth (y) and neck girth (x), both in inches. The least squares regression equation relating the two variables is $\hat{y}$ = 5.32 + 1.53 x. The standard deviation of the regression is s = 3.692.

-What is a 95% confidence interval for the average (or mean) chest girth for bears with a neck girth of 18 inches? The standard error of the fit, s.e.(fit), = 0.860.

A) (24.9, 40.9)
B) (28.1, 43.7)
C) (31.0, 34.7)
D) None of the above

Question 77

Use the following information for questions:
A sample of 19 female bears was measured for chest girth (y) and neck girth (x), both in inches. The least squares regression equation relating the two variables is $\hat{y}$ = 5.32 + 1.53 x. The standard deviation of the regression is s = 3.692.

-What is a 95% prediction interval for the chest girth of a bear with a neck girth of 18 inches? The standard error of the fit, s.e.(fit), = 0.860

A) (24.9, 40.9)
B) (28.1, 43.7)
C) (31.0, 34.7)
D) None of the above

Question 78

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A regression line that relates y = hand span (cm) and x = height (inches) is $\hat{y}$ = -1 + 0.3 x. The sample size was n = 5 adults. The standard deviation of the regression is s = 1 cm. For height = 60 inches, the standard error of the fit is s.e.(fit) = 1 cm.
-What is a 90% prediction interval for the hand span of a person whose height is 60 inches?

Question 79

Use the following information for questions:
A regression line that relates y = hand span (cm) and x = height (inches) is $\hat{y}$ = -1 + 0.3 x. The sample size was n = 5 adults. The standard deviation of the regression is s = 1 cm. For height = 60 inches, the standard error of the fit is s.e.(fit) = 1 cm.
-What is a 90% confidence interval for the mean hand span of people who are 60 inches tall?

Question 80

Use the following information for questions:
A car salesman is curious if he can predict the fuel efficiency of a car (in MPG) if he knows the fuel capacity of the car (in gallons). He collects data on a variety of makes and models of cars. The scatterplot shows that a linear model is appropriate. SPSS output is provided below.

-How many cars were included in the study?