# Calculate correlations; least squares lines, make prediction

See attached Minitab file.

The data set CSDATA contains information about all 224 students who entered a large university in a single year and who planned to major in a computer science. We are interested in predicting GPA (grade point average) after three semesters of college from information available before the student enters college. To do this effectively, we must use several explanatory variables together. This is multiple regression. In this Case Study, You will look at the individual explanatory variables.

A. Correlations. What are the correlations of all the explanatory variables with GPA? Explain why knowing the correlations tell us which variables will best predict GPA in a regression with just one explanatory variable. What are the two best predictor variables? Does your finding seem reasonable for computer science majors?

B. Prediction. Make scatterplots, with the least-squares line added, for GPA versus each of the two best explanatory variables. How well do each of these variables predict GPA? Do these scatterplots contain unusual observations? In what way is each of these observations

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#### Solution Summary

The data set CSDATA contains information about all 224 students who entered a large university in a single year and who planned to major in a computer science. We are interested in predicting GPA (grade point average) after three semesters of college from information available before the student enters college. To do this effectively, we must use several explanatory variables together. This is multiple regression. In this Case Study, You will look at the individual explanatory variables. Calculate Correlations; construct least squares lines, make prediction and plots

Linear Correlation, Regression Lines and Measures of Variation

1) Testing for a Linear Correlation

Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from the table below using a=0.05. Determine whether the is sufficient evidence to support a claim of a linear correlation between the two variables.

Airline Fares Listed below are the costs (in dollars) of flights from New York (JFK) to San Francisco for US Air, Continental, Delta, United, American, Alaska, and Northwest. Use a 0.05 significance level to test the claim that there is no difference in cost between flights scheduled one day in advance and those scheduled 30 days in advance. What appears to be a wise scheduling strategy?

Flight scheduled 30 days advance 244 260 264 264 278 318 280

Fight scheduled one day in advance 456 614 567 943 628 1088 536

Create scatter plot

2) Finding the Equation of the Regression Line and Making Predictions

In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in

CPI and Subway Fare ; Find the best predicted cost of a slice of pizza when the consumer price index is 182.5 in the year 2000

CPI 30.2 48.3 112.3 162.2 191.9 197.8

Pizza 0.15 0.35 1.00 1.35 1.50 2.00

3) Finding the Equation of the Regression Line and Making Predictions

In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in

Commuters and Parking Space The Metro-North Station of Greenwich, CT has 2804 commuters . Find the best predicted number of parking spots at that station. Is the predicted value close to the actual value of 127?

Commuters 3453 1350 1126 3120 2641 277 579 2532

Parking Spots 1653 676 294 950 1216 179 466 1454

4) Finding Measures of Variation

Find (a) explained variation, (b) unexplained variation,(c) total variation, (d) coefficient of determination,and (e) standard error of estimate Se, In each case, there is sufficient evidence to support a claim of a linear correlation so that it is reasonable to use the regression equation when making predictions

CPI and Subway Fare The consumer price index and the cost of a slice of pizza from table 10-1

CPI 30.2 48.3 112.3 162.2 191.9 197.8

Pizza 0.15 0.35 1.00 1.25 1.75 2.00