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3. (30 points) Suppose that we have two quiz scores for n6 students in an introductory statistics course: Quiz #1 score (z) and Quiz #2 score (s). The data are given in Table For the questions that follow, you are to calculate these by hand; however, you are encouraged to also use R to confirm that your answers are correct. i 1 23 4 5 6 707580808590 7582808690 91 Table 2: Quiz scores. (a) What is the estimated simple linear regression equation for these data? b) For each individual observation, calculate the predicted value gi and the residual ei. It might be easiest to summarize the values in a table. c) Calculate the SSE, the sum of squared errors (d) Calculate the sample estimate of the variance, ?2, for the regression model. (e) Calculate the sample standard deviation and write a sentence that interprets this value. (f) Calculate the value of R2. To start, you will have to calculate the value of the SSTO. Write a sentence that interprets the value of R2 in the context of these data.

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=20 D (4-3) 2. 32 l6 8 4 84 2 2 千 9 2 = SSE 6-2 n-2 df oy e

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