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.

1. the fitted equation, and residuals
2. a plot of Yvs X,
3. a residual plot of evs X,
4. a test of whether deflections are associated with area of the wires,
5. Normal Probability Plot of the residuals
6. Shapiro-Wilk test for normality
7. Brown-Forsyth test for constant variance (use areaWire ? 66 and areaWire ? 53 as groups)
8. Breusch-Pagan Test for constant variance
9. F-test for lack-of-fit
10. Durbin-Watson test (assuming this is the run order of the physical experiment)
11. Obtain "best" power transformation method, based on Box-Cox transformations
12. Obtain simultaneous 95% Confidence Intervals forb₀, b₁
13. Obtain an approximate 95% Confidence Interval for the Area of the coupling, when a deflection of 115 was observed (See section 4.6)
14. Obtain X'X, X'Y, (X'X)^-1, beta-hat, MSE, and s²{beta-hat}

A B 1 coupling areaWire defGalv 2 152 85 152 81.5 152 83.5 125 102 125 90.5 125 98.5 99 109 99 115.5 10 66 131 11 66 128.5 12 66 138.5 13 53 149 14 53 149 15 53 147 16 35 152.5 17 35 158.5 18 35 151 19 25 161 20 25 170 21 25 166 22 17 185.5 23 17 192