# Homework 15 - Z68144 Graded Homework 15 You have submitted...

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Z68144 Graded Homework 15 You have submitted this Homework 1 time (including this time). You may submit this Homework a total of 40 times and receive full credit. This homework covers material about the correlation coefficient in simple regression and violations of assumptions about errors, material tha can be found on pages 86-90 in your course packet. Question #1 Look at the example on slide 41 (page 87) of the course packet. They want you to do a test on the correlation coefficient (that is, a test to see if any linear relationship exists between two variables) between student population size and pizza sales, based on the Armani Pizza example. The data is provided here . Answer the following questions based on your findings. 1. The sample correlation coefficient between sales in thousands of dollars and the number of students in thousands is given by 0.963366334 . If sales was measured in millions of dollars instead of thousands of dollars then the correlation coefficient o would stay the same o would go up o cannot be computed o would go down . 2. Suppose you would like to test whether the population correlation coefficient between number of students and sales is 0. The value of the test statistic for testing this hypothesis is 10.16004421 and the p-value is 7.53839E-06 = 7.53839e-06 . This test statistic and p-value are the same as the test statistic and p-value for the test of the regression slope coefficient. Then, based on these results, you can say that: a linear relationship does exist between pizza sales and the size of student population. 3. Now do the F-test for overall validity of the model (slide 30 on page 84) . What is the value of the test statistic? 103.2264983 and the corresponding p-value is 7.53839E-06 = 7.53839e-06 . This p-value is the same as the p-value for the individual t-test of the regression

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slope coefficient. You received a raw score of 100% on this question. Question #2 Look at the example on slide 40 (page 86) of the course packet. Do a test on the correlation coefficient (that is, a test to see if any linear relationship exists between two variables) between the odometer milage and used car prices, based on the Car Sale Price example. Partial results are provided here . Answer the following questions based on your findings. 1. The sample correlation coefficient between used car sale price and the odometer mileage is given by <no answer> . 2. Suppose you would like to test whether the population correlation coefficient between odometer mileage and used car price is 0. The value of the test statistic for testing this hypothesis is -13.49465085 and the p-value is 4.44346E-24 = 4.44346e-24 . 3. Now do the F-test for overall validity of the model (slide 30 on page 84) . What is the value of the test statistic? 182.1056015 . The numerator and denominator degrees of freedom for this F-test are repectively 1 and 98 . The corresponding p-value is 4.44346E-24 = 4.44346e-24 .
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