Question 1

An airline has determined that the relationship between the number of passengers (x) on a flight and the total weight (y) (in pounds) of luggage stored in the baggage compartment can be estimated by the least-squares regression equation y = 250 + 27x. Predict the weight of luggage for a flight with 125 passengers.

Accepted Answer

The equation y = 250 + 27x is used to predict the weight of luggage. For 125 passengers, y = 250 + 27(125) = 3625 pounds.

Question 2

To determine the effectiveness of group study sessions, a college instructor gathers data on hours of attendance and exam scores for students in the class. Which variable, hours of attendance or exam scores, would be the response variable for a least-squares regression equation?

Accepted Answer

The response variable is the variable that is being predicted or explained by the explanatory variable. In this case, the goal is to determine the effectiveness of group study sessions on exam performance, so the response variable is the exam scores. The hours of attendance would be the explanatory variable, as it is hypothesized to explain or predict the exam scores. Therefore, the response variable for a least-squares regression equation would be exam scores.

Question 3

The least-squares regression equation y = 50 + 0.1x gives the yield in bushels per acre of corn when x pounds of fertilizer are applied. Predict the yield for a farmer who plans to use 320 pounds of fertilizer.

Accepted Answer

To predict the yield for 320 pounds of fertilizer, substitute x = 320 into the equation: y = 50 + 0.1(320) = 50 + 32 = 82 bushels per acre.

Question 4

Use the following scatterplot to answer the Questions: 
-What conclusions can you reach if you hear 18 chirps a minute?

Accepted Answer

The number of chirps per minute can be used to estimate the temperature in Fahrenheit using Dolbear's Law. According to this law, 18 chirps per minute would correspond to a temperature of approximately 87 degrees Fahrenheit.

Question 5

To choose advertising media, a marketing analyst studies the relationship between a consumer's income and the amount spent on restaurant dining. Which variable, consumer's income or dining expenditures, would be the response variable for a least-squares regression equation?

Accepted Answer

The variable being studied (dining expenditures) would be the response variable, as it is the dependent variable that is being affected by the independent variable (consumer's income).

Question 6

A data set has $\bar{x}$ = 3, $\bar{y}$ = 10, S_x=1 S_y =3 r = 0.45 . Which of the following point is on the least-squares regression line?

Accepted Answer

Using the formula for the equation of the least-squares regression line, we have:
$\hat{y} = b_1x +b_0$
where,
$b_1 = r \frac{S_{y}}{S_{x}}$
and
$b_0 = \bar{y} - b_{1}\bar{x}$
Plugging in the given values,
$b_1 = 0.45 \frac{S_{y}}{S_{x}}$
Also, for any point on the least-squares regression line, the coordinates should satisfy this equation. 
Thus, checking the options
A) (10,3): $\hat{y} = 0.45(\frac{S_{y}}{S_{x}})(10) + \bar{y} - 0.45(\frac{S_{y}}{S_{x}})(3) = 6.15\neq3$
B) (3,1): $\hat{y} = 0.45(\frac{S_{y}}{S_{x}})(3) + \bar{y} - 0.45(\frac{S_{y}}{S_{x}})(3) = 10\neq1$
C) (1,3): $\hat{y} = 0.45(\frac{S_{y}}{S_{x}})(1) + \bar{y} - 0.45(\frac{S_{y}}{S_{x}})(3) = 7.65\neq3$
D) (3,10): $\hat{y} = 0.45(\frac{S_{y}}{S_{x}})(3) + \bar{y} - 0.45(\frac{S_{y}}{S_{x}})(3) = 10$

Thus, only point D (3,10) is on the least-squares regression line.

Question 7

Use the following scatterplot to answer the  Questions:

-What can you say about the correlation of the data?

Accepted Answer

The scatterplot shows that the data points are scattered randomly and there is no clear linear pattern. This suggests that the correlation between the two variables is low, making choice C the best option. There is not enough evidence to suggest a positive or negative correlation, so choices A and B can be ruled out. The data is not completely random, so choice D can also be ruled out.

Question 8

Use the following scatterplot to answer the Questions:

-For the scatterplot shown above, what y value would you expect to be paired with x = 9?

Accepted Answer

Based on the general trend of the scatterplot, as x values increase, y values tend to decrease. At x = 9, the scatterplot intersects the trendline at approximately y = 450. Therefore, we can reasonably expect the y value to be paired with x = 9 to be around 450.

Question 9

A typing service keeps data on the number of pages (x) in a manuscript and the length of time (y) (in hours) it takes to complete the typing. The least-squares regression line for the data is given by y = 20 + 0.273x. Use this to predict the amount of hours needed to type a 40-page manuscript.

Accepted Answer

Using the equation y = 20 + 0.273x, we can substitute x = 40 to find the predicted time for typing a 40-page manuscript:
y = 20 + 0.273(40) = 30.92
Therefore, the predicted time for typing a 40-page manuscript is approximately 30.92 hours, which is answer choice C.

Question 10

Use the following scatterplot to answer the  Questions:

-What can you say about the association of the variables?

Accepted Answer

The statement "the variables are not linearly correlated" suggests that there might be a relationship between the variables, but it does not follow a straight-line pattern. This can occur in situations where the relationship is more complex or follows a different type of mathematical function, such as a quadratic or exponential relationship. Without specifying the nature of the correlation (positive, negative, or none), this option implies that traditional linear correlation measures (like Pearson's correlation coefficient) might not capture the nature of the relationship effectively.

Question 11

Suppose you are taking a survey of young children. If you measure their height and their weight, what do you expect to determine about these data?

Accepted Answer

We would expect to determine a positive correlation between height and weight in young children. As children grow taller, they also tend to gain weight as a result of increased muscle and bone development. Therefore, we would expect to see a positive trend in the data as height increases, so does weight.

Question 12

Use the following scatterplot to answer the Questions: 
-What can you say about the slope of the least-squares regression line?

Accepted Answer

The scatterplot shows a positive correlation between the two variables, therefore the slope of the least-squares regression line is positive.

Question 13

Use the following scatterplot to answer the  Questions:

-What can you say about outliers in the data set?

Accepted Answer

There are no data points that appear to be significantly away from the main cluster, so there are no apparent outliers in the data set.

Question 14

Use the following scatterplot to answer the Questions:

-For the scatterplot shown above, what can you say about the correlation?

Accepted Answer

The correlation is between 0 and 1 if the scatterplot shows a positive linear relationship, indicating that as one variable increases, the other tends to increase as well.

Question 15

A university admissions counselor wishes to predict the performance of freshmen by considering their SAT scores. Which variable, freshman GPA or SAT score, would be the explanatory variable in a least squares regression equation?

Accepted Answer

The SAT score would be the explanatory variable as it is being used to predict freshman performance (measured by GPA).

Question 16

A data set has $\bar{x}$ = 2, $\bar{y}$ = 7, S_x = 3, S_y = 3 r = 0.95 Which of the following point is on the least-squares regression line?

Accepted Answer

The least-squares regression line passes through the point $(\bar{x}, \bar{y}) = (2, 7)$. Therefore, option B is on the line. Options A, C, and D are not necessarily on the regression line, as they may have different residual values.

Question 17

A bank collects data on the savings and incomes of families to predict an expected increase in certificate of deposit accounts due to a 10% increase in salaries of employees at a local company. Which variable, savings or income, would be the explanatory variable?

Accepted Answer

The explanatory variable is the variable that is believed to have an effect on the response variable (in this case, the expected increase in certificate of deposit accounts). In this scenario, the explanatory variable is the change in family income due to the 10% increase in salaries of employees at a local company. The bank believes that this increase in income will lead to an increase in savings and ultimately an increase in certificate of deposit accounts. Therefore, family income is the explanatory variable.

Question 18

For professional baseball players, one would expect a negative correlation between:

Accepted Answer

One would expect that the more errors a player makes, the lower their salary would be, as errors can directly affect the outcome of games and indicate a lack of skill or effort on the player's part. Therefore, there would be a negative correlation between number of errors and salary. The other choices do not necessarily have a clear correlation and could vary among players and teams.

Question 19

Use the following scatterplot to answer the Questions: 
-What can you say about the correlation?

Accepted Answer

The scatterplot shows a positive linear relationship between the two variables, indicating a correlation between 0 and 1. However, it is not strong enough to be exactly 1, hence choice B can be ruled out. Choices A and D are incorrect as the correlation cannot be greater than 1 or negative.

Question 20

While you are running on a treadmill, you would expect a positive correlation between:

Accepted Answer

The longer you spend running on a treadmill, the more calories you are likely to burn. This is because the amount of energy (in calories) that you burn during exercise is related to the duration of the activity. As you exercise for a longer time, your body uses up more energy, which leads to an increase in the number of calories you burn. Therefore, there is a positive correlation between the time you spend running on a treadmill and the calories you burn.

B and C are not correct choices as there is no direct relationship between the time you spend running on a treadmill and your weight or average running speed.

Quiz 6: Exploring Data: Relationships

To determine the effectiveness of group study sessions, a college instructor gathers data on hours of attendance and exam scores for students in the class. Which variable, hours of attendance or exam scores, would be the response variable for a least-squares regression equation?

The least-squares regression equation y = 50 + 0.1x gives the yield in bushels per acre of corn when x pounds of fertilizer are applied. Predict the yield for a farmer who plans to use 320 pounds of fertilizer.

Use the following scatterplot to answer the Questions: -What conclusions can you reach if you hear 18 chirps a minute?

To choose advertising media, a marketing analyst studies the relationship between a consumer's income and the amount spent on restaurant dining. Which variable, consumer's income or dining expenditures, would be the response variable for a least-squares regression equation?

A data set has xˉ\bar{x}xˉ = 3, yˉ\bar{y}yˉ​ = 10, Sx=1 Sy =3 r = 0.45 . Which of the following point is on the least-squares regression line?

Use the following scatterplot to answer the Questions: -What can you say about the correlation of the data?

Use the following scatterplot to answer the Questions: -For the scatterplot shown above, what y value would you expect to be paired with x = 9?

A typing service keeps data on the number of pages (x) in a manuscript and the length of time (y) (in hours) it takes to complete the typing. The least-squares regression line for the data is given by y = 20 + 0.273x. Use this to predict the amount of hours needed to type a 40-page manuscript.

Use the following scatterplot to answer the Questions: -What can you say about the association of the variables?

Suppose you are taking a survey of young children. If you measure their height and their weight, what do you expect to determine about these data?

Use the following scatterplot to answer the Questions: -What can you say about the slope of the least-squares regression line?

Use the following scatterplot to answer the Questions: -What can you say about outliers in the data set?

Use the following scatterplot to answer the Questions: -For the scatterplot shown above, what can you say about the correlation?

A university admissions counselor wishes to predict the performance of freshmen by considering their SAT scores. Which variable, freshman GPA or SAT score, would be the explanatory variable in a least squares regression equation?

A data set has xˉ\bar{x}xˉ = 2, yˉ\bar{y}yˉ​ = 7, Sx = 3, Sy = 3 r = 0.95 Which of the following point is on the least-squares regression line?

A bank collects data on the savings and incomes of families to predict an expected increase in certificate of deposit accounts due to a 10% increase in salaries of employees at a local company. Which variable, savings or income, would be the explanatory variable?

For professional baseball players, one would expect a negative correlation between:

Use the following scatterplot to answer the Questions: -What can you say about the correlation?

While you are running on a treadmill, you would expect a positive correlation between:

A data set has $\bar{x}$ = 3, $\bar{y}$ = 10, S_x=1 S_y =3 r = 0.45 . Which of the following point is on the least-squares regression line?

A data set has $\bar{x}$ = 2, $\bar{y}$ = 7, S_x = 3, S_y = 3 r = 0.95 Which of the following point is on the least-squares regression line?