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Exam 17: Simple Linear Regression

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Question 21

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Sarah collected the data on heights and weights from 100 graduate students. Based on the data, she built a simple linear regression model to predict weight (in lbs) from height (in inches) . The regression line is found to be Y' = 4X - 136. Which of the following statements is the correct interpretation of the equation?

A) When weight increases by 1 lb, height is expected to increase by 4 inches.
B) When weight decreases by 4 lbs, height is expected to increase by 1 inch.
C) When height increases by 1 inch, weight is expected to increase by 4 lbs.
D) When height increases by 4 inches, weight is expected to decrease by 1 lb.

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Question 22

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The standardized regression slope ( $b_{Y X}^{*}$ )

A) may never be negative.
B) may never be greater than +1.00.
C) is always equal to 0.
D) None of the above.

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Question 23

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In simple linear regression, if r_XY = .3, the proportion of variation in Y that is not predictable from X is which one of the following?

In which of the following situations is it most appropriate to use the simple linear regression model?

Dr. Watt is studying the relation between the percentage of a population who has a bachelor's degree (X) and the average income (Y) in 108 cities. After fitting a simple linear regression model, he decides to assess whether the assumptions of the model are reasonably satisfied. Below is one of the plots he uses to assess the assumptions. (a) What assumption(s) is Dr. Watt trying to assess using this plot? (b) Based on the plot, is there any indication of assumption violations? If so, which assumption(s) has (have) been violated? (c) What are the possible consequences of the assumption violation(s)? (d) Suggest at least one solution to fix the problem.

The regression line for predicting college GPA from SAT scores is found to be Y' = 0.0016X + 0.6. Karen's SAT score is 1800, and Mary's SAT score is 1600. What is the predicted difference in their college GPA?

Derek is studying the relation between the selling price of a house (in dollars) (Y) and the age of the house (in years) (X) . It is shown that r_XY = - 0.2, $\bar{X}$ = 40, $\bar{Y}$ = 460,000. If Derek's own house was constructed 50 years ago, then the predicted selling price of his house based on simple linear regression would be

You are given the following pairs of scores on X (Pretest score) and Y (Posttest score). $\begin{array}{cc}\hline X & Y \\\hline 65 & 74 \\82 & 87 \\70 & 82 \\46 & 53 \\55 & 69 \\75 & 81 \\\hline\end{array}$ a. Find the linear regression model for predicting Y from X. b. Use the prediction model obtained to predict the value of Y for a new person who scored 80 on the pretest.

Dr. Watt is studying the relation between the percentage of a population who has a bachelor's degree (X) and the average income (Y) in 108 cities. After fitting a simple linear regression model, he decides to assess whether the assumptions of the model are reasonably satisfied. Below is one of the plots he uses to assess the assumptions. (a) What assumption(s) is Dr. Watt trying to assess using this plot? (b) Based on the plot, is there any indication of assumption violations? If so, which assumption(s) has (have) been violated? (c) What are the possible consequences of the assumption violation(s)? (d) Suggest at least one solution to fix the problem.

If the slope of the estimated regression line is positive, the correlation between X and Y

If the homogeneity assumption is violated, the possible consequences include

In simple linear regression, the unstandardized regression line will always pass

Dr. Guinea was studying the relation between the amount of caffeine intake and people's performance on a difficult task. He found out that as the amount of caffeine intake increases, the time to finish the task first decreases, and then increases. If he used the data to fit a linear regression model, which assumption would likely be violated?

Which assumption(s) involved in simple linear regression can be assessed by examining the residual plot (e_i vs. X_i) ?

You are given the following pairs of scores on X (height in inches) and Y (weight in lbs). Perform the following computations using $\alpha$ = .05. $\begin{array}{cc}X & Y \\\hline 66 & 140 \\69 & 155 \\72 & 195 \\74 & 160 \\72 & 155 \\67 & 145 \\66 & 135 \\71 & 170 \\70 & 130 \\68 & 170 \\72 & 190 \\69 & 145 \\73 & 155 \\68 & 150 \\68 & 130 \\69 & 145 \\69 & 150 \\66 & 120 \\62 & 131 \\62 & 120 \\64 & 102 \\68 & 110 \\63 & 116 \\64 & 125 \\62 & 110 \\\hline\end{array}$ a. The regression equation of Y predicted by X. b. Test of the significance of X as a predictor. c. Plot Y versus X. d. Compute the residuals. e. Plot residuals versus X.