1. Nine students in a college math class took a pre-test. We are interested in whether the pre-test is useful for predicting final course percentage. Here are the students' scores: Student 1 2 3 4 5 6 7 8 9 Pre-Test 83 81 70 79 69 61 88 72 86 Final Course Percentage 68 59 72 75 55 52 81 63 70 (a) Use R to make a scatterplot of the data. Does it seem like a straight line model is reasonable? (b) Use R to find the correlation, r, for these data. (c) Assuming a straight-line model, use R to compute estimates of the intercept (So) and slope (81). (d) Make a scatterplot of the data, this time including the regression line. Set the x-axis and y-axis limits so that (0. 0) is included in your plot. (e) If a student scores 80 on the pre-test, what does the model predict will be that student's final score? (f) Is it plausible the true slope is 0? That is, what do the data say about Ho : 81 = 0? (g) Find a 95% confidence interval for 31.1. Math pre = c(83, 81, 70, 79, 69, 61, 88, 72, 86) final = c(68, 59, 72, 75, 55, 52, 81, 63, 70) 1a. model = 1m(final ~ pre) plot (x=pre, y=final, xlab = "Pre-test scores", ylab = "Final test scores") abline(model, col="red") O O O 0 Final test scores # O 60 65 70 75 80 85 Pre-test scores From the way the points are spread out through the graph, especially without the line, it's hard to tell with complete certainty that the model is a straight line. However, I would say yes given that they general line they are fall in is straight. 1b. cor (x=pre, y=final)## [1] 0.7056401 1c. model ## ## Call: ## 1m(formula = final ~ pre) ## ## Coefficients: ## (Intercept) pre # # 8. 6029 0. 7512 1d. plot (x=pre, y=final, xlab = "Pre-test scores", ylab = "Final test scores ", xlim=c(0, 100), ylim=c abline(model, col = "blue") 100 Final test scores O 0 20 40 60 80 100 Pre-test scores