Answer Key to "Inference for Regression"

AP Statistics / Mr. Hansen

Name: _________________________________

Corrected Answer Key (4/26/99) for "Inference for Regression" Worksheets
(sketches of solutions, with most of the work and details missing)

Note:

Your work is what will be graded. These answers are meant primarily to reassure you that you’re on the right track.

Be sure to state the assumptions that we make whenever performing inference for regression.

At the places marked *, you should have checked the residual plot to make sure there are no glaring patterns. Greater density near the center line of the residual plot is OK and is to be expected.

(1)	Scatterplot shows positive linear relationship. Check residual plot, too—no patterns evident.*
(2)	xbar = 55, ybar = 52.333, s_x = 18.708, s_y = 7.367
(3)	r = 0.958, yhat(x) = 31.590 + 0.377x
(4)	0.958 (7.367/18.708) = 0.377 ü
(5)	s² = MSE = 5.605
(6)	s_b1 = 0.0566 (note corrected value)
(7)	(0.220, 0.534)
(8)	There is good evidence (t = 6.664, df = 4, P = 0.0013) to reject H₀ in favor of the one-sided alternative.
(9)	omit
1.	b₁ = 0.15428; check scatterplot to verify positive linear association, residual plot to verify absence of patterns*
2.	t = 12.503, p = 0.000008
3.	s_b1 = 0.01234
4.	(0.124, 0.184) (note corrected values)
5.	omit
1.(a)	y = –310.999 + 150.894x; check scatterplot to verify positive linear association, residual plot to verify absence of patterns*
(b)	SSE = 97,361.232
(c)	s_b1 = 17.152
(d)	H₀: b = 0 Note: Normally we would say b₁ instead of b, but the preamble for this problem used b to denote the true slope.
(e)	(114.53, 187.25)
(f)	There is strong evidence (t = 8.798, df = 16, P = 0.00000008) to reject H₀ in favor of the one-sided alternative H_a: b >0.
2.(a)	First, check scatterplot to verify negative linear association, and check residual plot to verify absence of patterns.* H₀: b₁ = 0 H_a: b₁ < 0 There is good evidence (t = –3.096, df = 6, P = 0.0106) that image quality is negatively associated with average reading time.
(b)	H₀: b₁ = –0.25 H_a: b₁ ¹ –0.25 There is no evidence (t = –0.875, df = 6, P = 0.415) that the slope differs from –0.25. (Of course, this doesn’t prove b₁ = –0.25. All we can say is that there is insufficient evidence to reject that hypothesis.)