Regression Grading Key [Point number] {Comment}

(15.2) ANSCOMBE

(A) What is r now equal to? Explain. (Calculation and computation not necessary . . .)
[1] r = +1. Explanation: all data points fall directly on a line with an upward slope.

(B) How will removal of the influential outlier effect the slope of the model? . . . Explain.
[2] The slope will decrease. Explanation: When the outlier is in the data set, the least squares line is pulled toward it. (The least squares line is attempting to minimize the residuals.) The pull is removed when you remove the outlier point.

(15.4) NA-BP

(A) Regression model
[3] b = 26.18 / 0.409 = 64.01
[4] a = 174.2 - (64.01)(7.11) = -280.91
Model: = -280.91 + (64.01)(X)
[5] Interpretation of slope: For each unit increase in sodium consumption (g/day), the model predicts a 64.01 increase in systolic blood pressure (mm Hg). Proportionally, the model predicts a 6.4 increase in BP (mm Hg) per 0.1 increase in sodium consumption per day. {Inferences apply to source population only.}

Interpretation of intercept: This is where the linear model would cross the y axis at x = 0. It has no real biological interpretation, since a diet with absolutely no sodium is not compatible with life. In general, you should not extrapolate beyond the range of X.

(B) Prediction when X = 7.2
[6] = -280.91 + (64.01)(7.2) = 179.96 @ 180

(D) 95% confidence interval for the slope =
[9] 64.01 � (t_8,.975)(9.636) = 64.01 � (2.31)(9.636) = 64.01 � 22.26 = (41.75, 86.27).
[10] Interpretation of confidence interval: We are 95% confident parameter b falls between 41.75 and 86.27.

(E) SPSS replication. {Make sure you can interpret your output.}