Quiz 6 Name _____________________________Stat 217FORMULAS: 2nDFE DFSSMS SSTSSMR 211bSEbt SHOW YOUR WORK!!!1. The principal at Super High School is interested in using the number of hours a high schooler studieseach week to predict the student’s academic performance, rated on a scale from 0 to 10. The MINITABoutput follows:Predictor Coef StdErr T PConstant -0.1872 0.8834 -0.212 0.83350Hours 0.6100 0.1879 ***** 0.00268S = *** R-Sq = ****% R-Sq(adj) = 21.9%Analysis of VarianceSource DF SS MS F P Regression 1 ****** 101.39 10.541 0.00268Residual Error 33 317.39 ****Total 34 418.78(a) Write out the Simple Linear Regression model.(b) Write out the least-squares regression line for this problem.(c) How many students were used in this SLR?(d) The Simple Linear Regression model assumes the error terms have a constant variance, 2. Givean unbiased estimate of 2.(e) Calculate R2 .(f) Interpret the value of R2 . (g) What is the correlation between number of hours studied and academic performance? (h) Is there sufficient evidence to suggest that the slope, 1, is non-zero? Give the following regression output which help you answer this question: - the value of the test statistic - the distribution of the test statistic- the p-value 2. Does the evidence suggest that there is a linear relationship between number of hours studied and academic performance? Explain how you decided Yes or No. 3. Interpret the slope of the least squares regression line, b1 in terms of the problem.5 15 25 35-505Fitted ValueResidualResiduals Versus the Fitted Values(response is Price)4. William, a student at Super High, studies five hours a week. Based on the above regression output, what is Williams academic performance?5. A new student is starting at Super High this year. She studies 7 hours per week. The principal is not sure whether to use a confidence interval (CI) or a prediction interval (PI) to estimate this student’s academic performance at the end of the year. Do you recommend that the principal use a CI or a PI? Explain why your answer is correct.6. The constant variance assumption does not appear to be violated in the Residual versus Fitted Value plot shown on the right. Is there another assumption that appears to be violated for these data? Why or why not?7. For the least squares regression line, A. SSE is the smallest when compared to all other lines fit to the dataB. SSE is the largest when compared to all other lines fit to the dataC. SSE is the same when compared to all other lines fit to the
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