1. Download the Explosives dataset. Fit a simple linear regression, relating the deflection of galvonometer (Y) to the area of the wires on the coupling (X). Complete the following parts. Conduct all tests ata=0.05 significance level. Note: do not use the coupling number in the analysis.

a. the fitted equation, and residuals

b. a plot of Yvs X,

c. a residual plot of evs X,

d. a test of whether deflections are associated with area of the wires.

H₀: H_A: Test Statistic: Rejection Region P-value

e. Normal Probability Plot of the residuals

f. Shapiro-Wilk test for normality

H₀: P-value:

g. Brown-Forsyth test for constant variance (use areaWire 66 and areaWire 53 as groups)

H₀: H_A: Test Statistic: Rejection Region P-value

h. Breusch-Pagan Test for constant variance

H₀: H_A: Test Statistic: Rejection Region P-value

i. F-test for lack-of-fit

H₀: H_A: Test Statistic: Rejection Region P-value

j. Durbin-Watson test (assuming this is the run order of the physical experiment)

H₀: H_A: Test Statistic: P-value

k. Obtain "best" power transformation method, based on Box-Cox transformations and 95% CI

i. Obtain simultaneous 95% Confidence Intervals forb₀, b₁

b₀: ______________________________________ b₁: ______________________________________

m. Obtain an approximate 95% Confidence Interval for the Area of the coupling, when a deflection of 115 was observed (See section 4.6)

95% CI _________________________________________________________

n. Obtain X'X, X'Y, (X'X)^-1, beta-hat, MSE, and s²{beta-hat}

areaWire	defGalv
152	85
152	81.5
152	83.5
125	102
125	90.5
125	98.5
99	109
99	115.5
66	131
66	128.5
66	138.5
53	149
53	149
53	147
35	152.5
35	158.5
35	151
25	161
25	170
25	166
17	185.5
17	192