Lecture 9 Practice Problems PDF

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Lecture 9 Practice Problems Linear Regression and Correlation (1) For the following values of  and sample size, find the critical value for the correlation coefficient at  = 0.05, test the null hypothesis that  = 0, and interpret your findings. a)  = 0.78, n = 7 b)  = –0.32, n = 28 c)  = –0.20, n = 80 d)  = 0.41, n = 24

(2) Below is output from a linear regression using the yearly amount of milk produced in the US (in billions of pounds) as a predictor variable and the average price (in US $) per gallon as the response variable.

Interpolate the test for the Ho: slope = 0 and Ho: intercept = 0. Then, determine the regression equation from the output, and use it to predict the average price (in US $) per gallon for each of the following values of x: a) 150 billion pounds b) 175 billion pounds c) 180 billion pounds d) 210 billion pounds Finally, the above regression model yields a R2 = 0.67; interpret this value.

(3) Education researchers are interested in the relationship between video game playing, as measured by the number of hours per week spent playing video games, and performance in high school, as measured by a student’s GPA. The researchers randomly sample 40 seniors from Woodinville High School and ask each student how many hours per week they spend playing video games. The researchers then use the hours to predict GPA, from which they estimate a regression equation as 4.185 – 0.125x. (3a) For each hour of video game playing per week, what is the predicted change in GPA (3b) How many hours of video game playing per week would predict a GPA of 4.0? (3c) Students at Woodinville High School are placed on academic probation if their GPA is 2.0 or less. Based on the relationship above, how many hours of video game playing per week would cause a student to be placed on academic probation? (3d) The researchers calculate a value of R2 = 0.72. Interpret this value. (3e) Based on the above information, what is the estimate of the correlation coefficient, , between the hours per week spent playing video games and GPA? What are the critical values of at =0.05? Test the significance of  at =0.05 and interpret.

(4) The Department of Transportation conducts a study to see if the number of police cars patrolling the highway over a 5-mile length affects the average speed of cars on the highway, measured in miles per hour. After collecting data over a week, an analyst runs a regression analysis to predict the average speed of cars based on the number of police cars. Here is the regression output: Coefficient Intercept # Police Cars R2 = 0.75

Estimate 82.0 –3.0

t 29.1

P-value...