1.You think that there is a linear relationship between the average percentage assignment grades throughout the term (x) and the percentage grade on the final exam (y). You get both grades from 45 random students this term. You get the following summary data for this sample:

x = 71.5, sx = 10.83, y = 61.32, sy = 15.39, R = 0.82.

(a) Assuming that the conditions for a linear regression hold, find the linear model approximating the relationship between the average assignment grades and the grade on the final exam.

(b) Interpret the slope and intercept. If it does not make sense to interpret either, say so.

(c) Suppose the standard deviation of x, sx, decreases and all other values given above stay the same. How does your model change?

(d) The standard error for the y-intercept is 3.5291. What would the upper bound of a 95% confidence interval for the y-intercept be?