[1] A research analyst for an oil company wants to develop a model to predict miles per gallon based on highway speed. An experiment is designed in which a test car is driven at speeds ranging from 10 miles per hour to 75 miles per hour. The results are in the data set (SPEED.xls in the Doc Sharing).

1. Set up a scatter diagram for speed and miles per gallon.
2. Apply simple regression analysis, and then interpret the meaning of the slope b ₁ in this problem.
3. Interpret the meaning of the regression coefficient b ₀ in this problem.
4. Determine the coefficient of determination, r ² , and interpret its meaning.
5. How useful do you think this regression model is for predicting mileage?

[2] Refer to the data set given in [1]. Now assume a quadratic relationship between speed and mileage:

1. State the quadratic regression equation.
2. Predict the average mileage obtained when the car is driven at 55 miles per hour.
3. Determine the coefficient of multiple determination, r ² _Y.12 .
4. Determine the adjusted r ² .
5. Determine the adequacy of the fit of the model.
6. At the 0.05 level of significance, determine whether the quadratic model is a better fit than the linear regression model.

[3] Each year ninth-grade students in Ohio must take a proficiency test. The data (SCHOOL.xls in the Doc Sharing) contains data from 47 school districts in Ohio from 1994 to 1995 school year. The variables in the data set are:

– School District: Name of school district

– Percentage Passing: Percentage of students passing the ninth-grade proficiency test

– Percentage Attendance: Daily average of the percentage of students attending class

– Salary: Average teachers salary (dollars)

– Spending: Instructional spending per pupil (dollars)

1. Set up a scatter diagram using the percentage passing the proficiency test as the dependent variable and daily attendance as the independent variable. Discuss the scatter diagram.
2. Assuming a linear relationship, find the regression coefficients, b ₀ , b ₁ , and its regression equation.
3. Interpret the meaning of the slope b ₁ in this problem.
4. Find the standard error of the estimate.
5. Determine the coefficient of determination, r ² , and interpret its meaning.
6. Compute the coefficient of correlation r and interpret its meaning.
7. Perform a residual analysis on your results and determine the adequacy of the fit of the model.
8. At the 0.05 level of significance, is there evidence of a linear relationship between the independent variable and the dependent variable?
9. Set up a 95% confidence interval estimate of the population slope, \(\beta \) ₁ and interpret its meaning.
10. Repeat (a)--(i) using instructional spending as the independent variable.
11. Which of the two models is best at predicting the percentage of students who will pass the ninth-grade proficiency test? Write a short summary of your finding.

[4] In Problem [3], simple linear regression models were constructed to investigate the relationships between passing rate of the Ohio ninth-grade proficiency exam and two different independent variables. Develop the most appropriate multiple regression model to predict a school's passing rate. Be sure to perform a thorough residual analysis. In addition, provide a detailed explanation of the results, including a comparison of the most appropriate multiple

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