Practice Problems: Correlation and Linear Regression Answer

It is assumed that achievement test scores should be correlated with student's classroom performance. One would expect that students who consistently perform well in the classroom (tests, quizes, etc.) would also perform well on a standardized achievement test (0 - 100 with 100 indicating high achievement). A teacher decides to examine this hypothesis. At the end of the academic year, she computes a correlation between the students achievement test scores (she purposefully did not look at this data until after she submitted students grades) and the overall g.p.a. for each student computed over the entire year. The data for her class are provided below.

 Achievement G.P.A. 98 3.6 96 2.7 94 3.1 88 4.0 91 3.2 77 3.0 86 3.8 71 2.6 59 3.0 63 2.2 84 1.7 79 3.1 75 2.6 72 2.9 86 2.4 85 3.4 71 2.8 93 3.7 90 3.2 62 1.6

1. Compute the correlation coefficient. r = .524127623 or .52

2. What does this statistic mean concerning the relationship between achievement test prformance and g.p.a.? There is a moderate correlation between achievement test performance and g.p.a. As the achievement test scores go up, the g.p.a.s tend to increase as well and vice versa.

3. What percent of the variability is accounted for by the relationship between the two variables and what does this statistic mean? r2 = .27 The percent a variability is relatively low. Only 27 percent of the achievement test performance is related to the g.p.a (and vice versa). Seventy-three percent of the variability is left unexplained.

4. What would be the slope and y-intercept for a regression line based on this data? The slope would be .028430629 and the y-intercept would be .62711903.

5. If a student scored a 93 on the achievement test, what would be their predicted G.P.A.? 3.27; If they scored a 74? 2.73; An 88? 3.13

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