(i) Below are 4 scatter plots of an outcome y versus predictor x followed by fou
ID: 3055661 • Letter: #
Question
(i) Below are 4 scatter plots of an outcome y versus predictor x followed by four regression fit summaries labeled A, B, C and D·Label each plot according to the corresponding summary. 321 0123 -3 2 1 0 123 3210 123 -10 -5 0 5 10 residual standard error SSRISST R0.90 0.99 R2 = 0.93 R2 = 0.71 Dataset intercept slope || bo = 8.1, s,-0.11 | b1 = 2.1, sb1 = 0.066 | bo = 8.0, sbo = 0.10 | b1 = 2.0, sb1 0.017 bo-1.0, sbo-0.10 | bi-2.0, sh": 0.060 ll bo = 0.9, sto = 0.20 | bl = 1.9, sh = 0.120 A s= 1.08 8 1.01 s = 0.97 s=2.09 D (i) Suppose Y is linearly related to X. Which of the following is always true? Circle all that apply. (a) The 95% confidence interval for bo contains zero. (b) The 95% confidence interval for bi does not contain zero. (c) The marginal variance of Y is larger than the conditional variance of Y given X. (d) 0Explanation / Answer
i) The linear regression plots helps us understand how well the predictor variables fit the dependent variable.
The higher the R2 statistic, the better the predictor variables explain the variance in the dependent variable. In the 4th plot, the predictor variable seems to explain a very high variance in y, thus it would have a very high R2. Going by the same principal,
Plot 1 corresponds to regression fit D
Plot 2 corresponds to regression fit A
Plot 3 corresponds to regression fit C
Plot 4 corresponds to regression fit B
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