Hard Work Pays Off A study of students marks and how they ar

Hard Work Pays Off: A study of students\' marks and how they are related to the hours of study they put in was conducted. A sample of 300 students was surveyed and asked to (anonymously) report their final mark (out of 100) in their introductory statistics class, as well as the number of hours per week they spent studying for it. A scatterplot of the data with a linear regression line included, as well as a residual plot from a simple linear regression on the results are given below: Question 1 [6 marks] The coefficients summary table for the linear regression is: Coefficient Intercept Slope and the ANOVA table is: Source Hours/Week Residual Total t-Stat 15,56 33.95 P-Value Estimate 18.493 6.448 SD 1.189 0.190 F-Stat 1152.62 P-Value 0 df 59023.98 15260.14 74284.12 MS 59023.98 51.21 248.44 (a) What degrees of freedom go in the cell marked (2) in the ANOVA table? (b) Find a 95% confidence interval for the slope. (1 mark) (1 mark) (c) Someone suggests that even with no study at all. it should be possible to guess your way to a (1 mark) (d) Studying 8 hours/week is found to result in an average final mark of 18.493 6.448(8) 70.08 Moreover, a 95% confidence interval for the average final mark associated with 8 hours/week of studying is(68.94, 71.22). If you decide to study 8 hours/week, find a 95% prediction (1 mark) (e) Based on the residual plot, are there any issues with the underlying assumptions of linearity (1 mark) () If we fit a quadratic regression, the coefficient estimate for (Hours/Week)2 is -0.113 with a standard deviation of 0.093, Test whether the quadratic term is statistically significant. Would (1 mark) final mark of at least 20. Test this hypothesis .e., Ho: Intercept 2 20) interval for your final mark. and/or homoscedasticity? you suggest using the quadratic model over the linear one in this case?

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