2. For the data given, assume a model of the form: E(y) = 0 + 1x1 + 2x2 + 3x3 a.

Question

2. For the data given, assume a model of the form: E(y) = 0 + 1x1 + 2x2 + 3x3

a. Determine the least-squares multiple regression line.

b. What is the estimate of the standard deviation of the random error component () for this model and data?

c. Do you conclude that the interaction term is significant? Report the observed significance level and reach a conclusion using alpha = 0.05.

d. Find and interpret a 95% confidence interval for 3.

e. Test the overall adequacy of the model using alpha = 0.05.

Y X1 X2 X3 -333.43 -9.19 7.13 4.52 1178.36 9.81 7.99 9.06 -190.03 3.74 3.38 -8.56 -252.67 -7.04 2.09 9.58 -58.54 -1.1 1.67 -1.07 3.44 -3.59 -0.9 -9.76 270.57 6.72 0.97 2.19 -304.6 -8.68 6.13 3.01 -149.61 4.44 0.24 -8.42 325.25 6.25 4.57 1.72 107.34 9.3 5.13 -3.59 -85.56 4.9 -2.2 -5.43 -49.95 -0.38 -3.44 -1.17 -325.46 7.28 5.66 -9.65 -301.57 -6.46 -7.38 6.09 -58.46 -4.24 7.38 3.46 131.63 -0.61 7.65 3.88 51.44 1.21 -7.45 -8.95 -359.04 -1.97 7.82 -7.52 -367.16 -5.05 -5.72 8.88 43.75 5.25 -2.08 -0.39 -234.24 9.76 -8.01 -9.02 542.09 4.08 9.17 4.44 92.16 -7.47 -6.69 -3.03 -79.47 -3.8 9.72 1.88 -152.22 -1.48 -6.78 4.83 226.91 -7.13 -4.02 -8.84 -138.5 8.15 0.73 -6.77 -380.66 0.86 9.39 -8.82 -266 -1.62 8.08 -6.44 50.05 -4.27 -3.62 -4.68 -24.85 -0.99 -0.38 -1.85 17.03 -9.56 1.27 -9.49 -229.53 -7.64 5.78 8.59 -1.15 7.66 -4.62 -0.4 -63.87 5.07 1.5 -3.99 -14.39 4.79 7.13 -4.07 -394.04 -6.23 8.35 -7.87 -57.85 -3.89 8.82 2.58 19.34 1.01 2.58 -1.84 -389.24 -5.43 -9.24 7.51 -223.29 -8.26 1.22 1.99 -6.46 4.07 -4.14 -1.95 -8.36 3.91 -6.09 -0.3 -25.42 -2.9 -1.13 -4.4 -20.36 -3.81 -0.27 -8.26 -25.91 4.8 -8.72 -9.64 -56.94 -3 2.96 -0.15 69.39 7.55 -5.63 5.12 -197.69 3.13 2.09 -8.33 -246.99 -8.18 0.68 3.47 233.51 8.99 3.02 -0.28 42.47 -2.61 9.02 3.9 339.93 9.59 -0.88 3.85 48.25 0.95 7.23 0 -28.67 3.13 -5.3 0.84 -28.77 4.85 2.44 -4.21 -34.54 -2.61 -2.08 -3.93 74.76 6.37 5.39 -3.28 38.29 6.52 2.78 -2.9 351.47 9.78 1.74 2.21 24.08 2.38 -7.56 -9.66 185.25 -2.39 -9.9 -5.68 -358.39 -8.54 -7.41 5.85 -73.74 -5.21 0.84 -7.38 -94.47 -0.18 8.72 -3.05 -37.35 -1.28 -2.5 2.59 -378.03 -8.6 8.28 -2.36 684.65 3.25 7.41 9.64 -295.19 -9.44 -3.7 3.78 405.93 9.82 -0.23 4.66 604.61 5.69 5.87 6.59 -51.01 6.75 -7.93 3.69 -128.97 6.95 -9.9 -5.11 -255.08 -7.21 5.58 -7.9 -8.41 7.44 -5.33 1.01 -84.35 -2.55 -1.1 0 -150.57 -5.7 1.99 0.38 35.94 -6.23 -0.49 -7.92 106.9 4.54 -1.22 2.37 -108.02 -2.4 -0.1 -9.51 336.17 7.67 0.94 3.79 -7.34 3.32 0.18 -3.03 506.6 8.8 2.52 4.34 -111.55 2.18 1.63 -7.71 -387.42 -9.77 7.22 -3.46 -426.08 -6.63 9.6 -5.81 -305.31 -5.28 -3.24 8.66 186.53 2.78 5.95 0.74 136.33 -2.37 -5.59 -8.83 30.17 4.08 -3.31 1.58 -62.31 6.51 -7.76 0.88 40.42 -2.89 3.52 8.06 -335.64 -4.94 8.9 -6.98 445.77 -9.43 -7.84 -8.22 1032.84 9.33 5.65 9.41 218.44 -2.8 -9.55 -4.92 -186.22 0.69 -8.17 6.94 -68.53 -4.76 -1.26 -1.85 -94 -4.74 -6.84 0.87

Explanation / Answer

a) y^ = -1.003 + 23.9775 x1 + 3.111623755 *x2 + 11.93725563

b) standard error =

233.949844

d)

confidence interval

e) overall model has p-value = 2.75*10^(-8)

< 0.05 ,hence the model is significant

SUMMARY OUTPUT Regression Statistics Multiple R 0.570890921 R Square 0.325916444 Adjusted R Square 0.304851333 Standard Error 233.9498441 Observations 100 ANOVA df SS MS F Significance F Regression 3 2540442.053 846814.0175 15.47185969 2.7552E-08 Residual 96 5254322.837 54732.52955 Total 99 7794764.889 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -1.003714985 23.94056395 -0.041925286 0.966645334 -48.52535883 46.51792886 X1 23.97753283 3.994297006 6.002941893 3.43907E-08 16.04891594 31.90614973 X2 3.111623755 4.134031803 0.752685007 0.453480965 -5.094364518 11.31761203 X3 11.93725563 4.156438051 2.871991711 0.00501995 3.686791308 20.18771995

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