[11] 1. You and your favorite study buddies (12 of you altogether) decide to record the amount of time you spend preparing for the Stat 202 final exam. After the exam is done, you all compare your scores. To determine whether the studying had any impact, you conduct a regression analysis. A scatterplot showing these data as well as the line-of-best-fit is shown below: y-axis: score on test (no units) Y: B1:B12 80 60 40 200 400 600 800 x-axis: number of minutes spent studying Some details from the analysis: r = .5994 line of best fit: y = 0.0523x + 54.8265 SSE = 2261.03 [1] (a) Calculate the coefficient of determination for thisanalysis. [1] (b) to this model, how much benefit in test score should someone expect for every ten additional minutes spent studying? (c) According to this model, how long should someone need to study to get a score of 100? [2] (d) Which of these points, if any, would you suggest might be "influential points"? Justify your answer by describing how you would expect the line of best fit to change if these point(s) were removed (individually or together - however you'd like to approach it).Y2 31:312 40- 20- . 2 400 500 '0 _20 . 4o- . XI A1 :A12 Residual plot for the study. x-axis is the study tiAeEK-axis is the residual. [2] {e} Which ofthese points, if my, would count as \"regression outliers\"? Show how you reached this conclusion. (Reminder: n=12.} [2] A!) Your group decides to \"vote out\" two of the most conspicuous data points {you can probably guess which two). After doing so, the new line of best t is y = 0.0869x+ 51.238. Based on this new model, how many grade points should someone expect to gain from an additional 10 minutes of studying, and how many minutes of studying should be required to get a score of 100? [2]={g] The original model had a correlation of .5994 {n = 12}, and the new model [with two buddies evicted} had a correlation of .9522 {n = 10]. Determine the appropriate test conclusions {but not exact p-ualues] for two null hypothesis tests, one for each of these sample correlation coefficients, using a null hypothesis of Hg: p = 0 and an alternative hypothesis of HA: p = O and a significance threshold of a = 0.05. You might nd it usell to know that 1242223 St 5 2.228) = .95 for a tdimibutian with 10 degrees ofeedom, and P(2.306 S t 5 2.306) = .95 for a t-djstrihlrtion with 8 degrees of freedom