Question: Suppose r2 0 30 Since y 2 is
Suppose r2 = 0.30. Since ∑ (y - )2 is used in estimating the overall variability of the y values and ∑ (y - )2 is used in estimating the residual variability at any fixed value of x , explain why approximately the estimated variance of the conditional distribution of y for a given x is 30% smaller than the estimated variance of the marginal distribution of y.
Relevant QuestionsThe formula for the standard error of the sample slope b is se = s/∑(x - )2, where s is the residual standard deviation of y. a. Show that the smaller the value of s, the more precisely b estimates β. b. Explain why a ...Sketch a scatter-plot, identifying quadrants relative to the sample means as in Figure 12.5, for which (a) The slope and correlation would be negative and (b) The slope and correlation would be approximately zero. For the Georgia Student Survey data file on the text CD, the table shows the correlation matrix for college GPA, high school GPA, and daily time spent watching TV. a. Interpret r and r2 between time spent watching TV and ...For the Male Athlete Strength data file on the text CD, the prediction equation relating y = 1 repetition maximum bench press (1RMBP) in kilograms to x = repetitions to fatigue bench press (RTFBP) is = 117.5 + 5.86 x. a. ...Refer to the previous two exercises. Using significance level 0.05, what decision would you make? Explain how that decision is in agreement with whether 0 falls in the confidence interval. Do this for the data for both the ...
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