Exam 10: Correlation and Regression

Find the value of the linear correlation coefficient r -Two separate tests are designed to measure a student's ability to solve problems. Several students are randomly selected to take both tests and the results are shown below. Test A 48 52 58 44 43 43 40 51 59 Test B 73 67 73 59 58 56 58 64 74

Describe the error in the stated conclusion. -Given: There is no significant linear correlation between scores on a math test and scores on a verbal test. Conclusion: There is no relationship between scores on the math test and scores on the verbal test.

Provide an appropriate response. - $\text { Explain what is meant by the coefficient of determination, } r ^ { 2 } \text {. Give an example to support your result. }$

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. - $\mathrm { r } = 0.168 , \mathrm { n } = 15$

Provide an appropriate response. -When testing to determine if correlation is significant, we use the hypotheses $\mathrm { H } _ { 0 } : \mathrm { Q } = 0 . \mathrm { H } _ { 1 } : \mathrm { Q } \neq 0$ . Suppose the conclusion is to reject the null hypothesis. What does that tell us about the linear regression equation?

The paired data below consists of test scores and hours of preparation for 5 randomly selected students. The equation of the regression line is $\hat{\mathrm { y }} = 44.845 + 3.524 \mathrm { x }$ and the standard error of estimate is se $= 5.40$ . Find the $99 \%$ prediction interval for the test score of a person who spent 7 hours preparing for the test. x Hours of preparation 5 2 9 6 10 Test score 64 48 72 73 80

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. - $r = 0.981 , n = 25$

Use computer software to find the regression equation. Can the equation be used for prediction? -A wildlife analyst gathered the data in the table to develop an equation to predict the weights of bears. He used WEIGHT as the dependent variable and CHEST, LENGTH, and SEX as the independent variables. For SEX, he used male=1 and female=2. WEIGHT CHEST LENGTH SEX 344 45.0 67.5 1 416 54.0 72.0 1 220 41.0 70.0 2 360 49.0 68.5 1 332 44.0 73.0 1 140 32.0 63.0 2 436 48.0 72.0 1 132 33.0 61.0 2 356 48.0 64.0 2 150 35.0 59.0 1 202 40.0 63.0 2 365 50.0 70.5 1

Describe the error in the stated conclusion. -Given: Each school in a state reports the average SAT score of its students. There is a significant linear correlation between the average SAT score of a school and the average annual income in the district in which the school is located. Conclusion: There is a significant linear correlation between individual SAT scores and family income.