Deck 10: Correlation and Regression

Question 1

The two variables in a scatter plot are called the

A) independent variable and dependent variable.
B) relative frequency and relative proportion.
C) spread and pattern.
D) lines and points.

Answer 1

A

Question 2

A study was conducted to determine if there was a linear relationship between a person's age and his/her peak heart rate.
a. Draw the scatter plot for the variables.
b. Give a brief explanation of the type of relationship.

Answer 2

a. b. There appears to be a negative relationship between age and peak heart rate.

Question 3

The range of the correlation coefficient is from 0 to 1.

Answer 3

False

Question 4

Which of the following does not explain a possible relationship between variables when the null hypothesis is rejected?

A) direct cause-and-effect
B) uncorrelated
C) caused by a third variable
D) negative effect

Question 5

Daniel Wiseman, a scientist for Gres-Trans Corp., wants to determine if the flow rate of a particular material changes with different changes in temperature. The data is plotted in the figure below. What type of relationship exists between the flow rate and the change in temperature?

A) negative
B) positive
C) There is no relationship.
D) curvilinear

Question 6

Ten pairs of points yielded a correlation coefficient of 0.790. If , which of the following statements is correct if ? (Do not calculate a t-value.)

A) Because 0.790 is greater than 0.632, the null hypothesis is not rejected.
B) Because 0.790 is greater than 0.632, the null hypothesis is rejected.
C) Because 0.790 is greater than 0.602, the null hypothesis is not rejected.
D) There is no correlation between the variables.

Question 7

A positive relationship exists when both variables increase or decrease at the same time.

Question 8

A formula for the correlation coefficient r is __________.

Question 9

Test the significance of the correlation coefficient r at = 0.05 for the data below.

A) Accept because 8.03 < 3.18
B) Reject because 8.35 > 3.18
C) Accept because 8.35 < 2.78
D) Reject because 8.03 > 2.78

Question 10

The population correlation coefficient is computed by using all possible pairs of data values taken from a population.

Question 11

If there is a strong negative linear relationship between the variables, the value of __________ will be close to -1.

Question 12

__________ is a statistical method used to determine whether a relationship between variables exists.

Question 13

The rounding rule for the correlation coefficient requires two decimal places.

Question 14

Determine the type of relationship shown in the figure below.

A) positive
B) negative
C) multiple
D) There is no relationship.

Question 15

In a __________ relationship, as one variable increases, the other variable decreases, and vice versa.

Question 16

Compute the value of the correlation coefficient.

A) 0.933
B) 0.953
C) 0.907
D) 0.798

Question 17

An experiment is carried out to determine the relationship between the average speed (rpm) and power (hp) of a mixer. Draw the scatter plot for the variables.

Question 18

Draw a scatter plot for the following data that show the demand for a product (in hundreds) and its price (in dollars) charged in nine different cities.

Question 19

A study was conducted to determine if there was a relationship between the prices a non-member of a book club paid for various publications and the prices that a member paid for the same publications. The data gathered is shown below. Compute the value of the correlation coefficient.

A) 0.762
B) 0.857
C) 0.679
D) 0.932

Question 20

A correlation coefficient of 0.961 would mean that the values of x increase as the values of y decrease.

Question 21

The equation of a regression line is . What is the intercept of this line?

A) -4.6
B) 3.2
C) 4.6
D) 0

Question 22

Using a regression line of , a value of x = 3.6 would result in a predicted value of .

Question 23

A psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded.
a. Draw a scatter plot.
b. Determine the regression line equation and plot the regression line
on the scatter plot.

Question 24

A correlation coefficient r was calculated to be 0.830. The coefficient of nondetermination would be 0.170.

Question 25

A regression line was calculated as . The slope of this line is -3.2.

Question 26

If the correlation coefficient is 0.790, what is the explained variation?

A) 37.6%
B) 62.4%
C) 79%
D) 21%

Question 27

If the equation for the regression line is y' = 7x - 9, then a value of x = 2 will result in a predicted value for y of

A) 16
B) 25
C) 23
D) 5

Question 28

The formula for the coefficient of nondetermination is 1.00 - r² .

Question 29

If the equation for the regression line is y' = -4x + 3, then the slope of this line is

A) 6
B) 3
C) -1
D) -4

Question 30

The variation due to chance, found by the formula __________, is called the unexplained variation.

Question 31

A regression line can be used to show trends in data.

Question 32

If the equation for the regression line is y' = 8x + 4, then a value of x = -3 will result in a predicted value for y of

A) 4
B) -4
C) -20
D) 8

Question 33

If the correlation coefficient is 0.930, what is the unexplained variation?

A) 7%
B) 93%
C) 13.5%
D) 86.5%

Question 34

When r is not significantly different from 0, the best predictor of y is the ____________ of the data values of y.

Question 35

Find the equation of the regression line.

Question 36

A correlation coefficient r was calculated to be 0.610. The coefficient of determination would be approximately __________.

Question 37

If the equation for the regression line is y' = -8x + 3, then the intercept of this line is

A) 6
B) 3
C) -5
D) -8

Question 38

What is the value of when x = 3, if the equation of the regression line is ?

A) 4.73
B) 5.29
C) 34.5
D) 11.7

Question 39

Regression is a statistical method used to describe the nature of the relationship between variables.

Question 40

A realtor wanted to determine if there was a relationship between the size (in 100 square feet) of a new custom-built home and the price (in thousands of dollars) of the home.
a. Draw a scatter plot.
b. Determine the regression line equation and plot the regression line
on the scatter plot.

Question 41

A researcher has reason to believe that, for an experiment with 40 points, a 95% prediction interval would be of width 8. If the researcher wishes to run a more precise experiment that will result in a 95% prediction interval of width 4, then the researcher will require how many points?

Question 42

For a prediction value of y' from a specific value x, which of the following contribute to the prediction error?

A) The error in estimating the slope
B) The error in estimating the intercept
C) The standard error of the estimate
D) All of the above

Question 43

The standard error of the estimate is the standard deviation of the observed x-values about the predicted values.

Question 44

With enough variables, it is possible to get an R² value close to 1, even if the variables have no particular meaning in the model.

Question 45

Two researchers run identical experiments except researcher A collects twice as many points as researcher B. For a specific value x, researcher A estimates a y value of and researcher B estimates a y value of . We would expect that researcher A's 95% prediction interval around to be, in general,

A) wider than researcher B's 95% prediction interval around .
B) narrower than researcher B's 95% prediction interval around .
C) the same as researcher B's 95% prediction interval around .
D) wider than researcher B's 95% prediction interval around or narrower than researcher B's 95% prediction interval around , with equal probability.

Question 46

An analysis results in a multiple regression equation of y' = 73 + 24x₁+ 7x₂. We can conclude that

A) The variable x₁ is a very significant factor in this model.
B) The variable x₁ is a moderately significant factor in this model.
C) The variable x₁ is not a significant factor in this model.
D) This is insufficient information to assess the significance of x₁.

Question 47

As a researcher collects more and more data, the 95% prediction intervals in general

A) become narrower and narrower, with the widths getting closer and closer to 0.
B) become narrower and narrower, but the widths are always more than approximately 2 times the standard error of the estimate.
C) become narrower and narrower, but the widths are always more than approximately 4 times the standard error of the estimate.
D) become narrower and narrower, but the widths are always more than approximately 4 times the slope.

Question 48

The symbol used for the multiple correlation coefficient is R .

Question 49

If the correlation coefficient r is equal to 0.755, find the coefficient of determination and the coefficient of nondetermination.

A) The coefficient of determination is 0.430 and the coefficient of nondetermination is 0.570
B) The coefficient of determination is 0.869 and the coefficient of nondetermination is 0.131
C) The coefficient of determination is 0.570 and the coefficient of nondetermination is 0.430
D) The coefficient of determination is 0.131 and the coefficient of nondetermination is 0.869

Question 50

Compute the standard error of the estimate for the data below.

A) 1.54
B) 2.38
C) 3.46
D) 4.17

Question 51

If the correlation coefficient r is equal to 0.394, find the coefficient of nondetermination.

A) 0.845
B) 0.628
C) 0.275
D) 0.155

Question 52

The following data list ages of cars (in years) and monthly repair cost in dollars. What is the standard error of the estimate?

A) 6.36
B) 7.34
C) 8.75
D) 5.49

Question 53

The standard error of estimate can be used for constructing a(n) __________ interval about a value.

Question 54

In a multiple regression model y' = -11 + 5x₁ + 21x₂ + 11x₃ + 3x₄, if the x₁ value changes by 2, then the predicted value for y will change by

A) 10
B) 42
C) -1
D) 29

Question 55

The prediction interval around y' for a specific x is

A) a confidence interval for the true mean value of the y values that correspond to that x.
B) the value of y used to calculate the slope of the regression line.
C) the interval of values of x used to predict y'.
D) the difference between the value of y and the value of x.

Question 56

The total blood cholesterol concentrations, in mg/dL, are shown below for a random sample of six people. In the table below, x is the age of the subject and y is the subject's total cholesterol concentration. Find the 95% prediction interval when x = 59 years.

Question 57

Compute the standard error of the estimate for the data below. Round to the thousandths place.

A) 0.932
B) 1.404
C) 0.880
D) 0.444

Question 58

The standard error of estimate is the square root of the unexplained variation.

Question 59

If the correlation coefficient r is equal to 0.552, find the coefficient of nondetermination.

A) 0.695
B) 0.740
C) 0.429
D) 0.305

Question 60

If the correlation coefficient r is equal to 0.465, find the coefficient of determination.

A) 0.784
B) 0.682
C) 0.341
D) 0.216

Question 61

A multiple regression line was calculated in which x₁ was a student's grade point average and x₂ was a student's age. The multiple regression line was calculated as . If a student has a grade point average of 5.9 and is 20 years old, what is the predicted value of ?

A) 387.2
B) 400.1
C) 421.6
D) 615.5

Question 62

In a multiple regression model y' = -11 + 4x₁ + 11x₂ + 7x₃ + 3x₄, if the value of x₂ increases by 2 and the value of x₃ decreases by 5, then the predicted value for y will

A) decrease by 57.
B) increase by 57.
C) decrease by 13.
D) increase by 13.

Question 63

If there are three independent variables x₁, x₂, and x₃ available, then the value of R² for a multiple regression of y using x₁, x₂, and x₃ will always be smaller than the value of r² for a multiple regression of y using just x₁.