Answer Happy

3. With the following Statistics achievement test score and final Statistics course grade for a random sample of 10 college sophomore students: Student Test score Final grade 1 70 70 2 70 80 3 75 70 4 75 75 5 80 80 6 80 85 7 90 85 8 90 95 9 95 90 10 95 90 (a) Obtain the least squares estimators for the intercept and slope in a simple linear model. (b) What are the assumptions of the simple linear regression model? (c) Compute the least-squares estimators of a and for the linear model: Final grade = a + (Test score). (d) Provide the ANOVA table for linear regression. (e) Conduct the test of slope by specifying rejection region, test statistic, and conclusion with a Type I error rate= 0.05. (f) Obtain the 95% confidence interval for the Final grade when the Test score is 83. (g) Obtain the 95% prediction interval for the Final grade when the Test score is 85. (h) Calculate the sample correlation coefficient based on the tabulated data. (i) Using the above data, test the hypotheses Ho: p=0 versus H₁: p=0.