Refer to \"pr_3_data.xls\". Consider the linear model using Predictor variables X1, X2, and x4. That is, consider the model Y = beta o + beta1 x1 + beta2x2 + beta4x4 + e. Fit the above regression model to the data. Construct an ANOVA table and use it to test the hypothesis H0: beta1 = beta2 = beta4 = 0. Use a = 0.05. Find a 95% confidence interval for each of the regression coefficients in the model for this problem. Solution Coefficients: (Intercept) x1 x2 x3 x4 -97.2050 0.0416 12.2375 3.9221 10.3292 this gives the values of the beta\'s ( this has been done using R statistical software) lm(formula = y ~ x1 + x2 + x3 + x4) Residuals: Min 1Q Median 3Q Max -56.992 -12.178 2.223 11.977 44.482 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -97.2050 94.5222 -1.028 0.3280 x1 0.0416 2.0048 0.021 0.9839 x2 12.2375 6.1543 1.988 0.0748 . x3 3.9221 9.5509 0.411 0.6900 x4 10.3292 15.5752 0.663 0.5222 --- Signif. codes: 0.

1. Refer to "pr_3_data.xls". Consider the linear model using Predictor variables X1, X2, and x4.
That is, consider the model Y = beta o + beta1 x1 + beta2x2 + beta4x4 + e. Fit the above
regression model to the data. Construct an ANOVA table and use it to test the hypothesis H0:
beta1 = beta2 = beta4 = 0. Use a = 0.05. Find a 95% confidence interval for each of the
regression coefficients in the model for this problem.
Solution
Coefficients:
(Intercept) x1 x2 x3 x4
-97.2050 0.0416 12.2375 3.9221 10.3292
this gives the values of the beta's ( this has been done using R statistical software)
lm(formula = y ~ x1 + x2 + x3 + x4)
Residuals:
Min 1Q Median 3Q Max
-56.992 -12.178 2.223 11.977 44.482
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -97.2050 94.5222 -1.028 0.3280
x1 0.0416 2.0048 0.021 0.9839
x2 12.2375 6.1543 1.988 0.0748 .
x3 3.9221 9.5509 0.411 0.6900
x4 10.3292 15.5752 0.663 0.5222
---
Signif. codes: 0