MINITAB was used to fit the model Y = beta_0 + beta_1 x_1 + beta_2 x_2 + beta_3

Question

MINITAB was used to fit the model Y = beta_0 + beta_1 x_1 + beta_2 x_2 + beta_3 x_3 + beat_4 x_4 + epsilon to n = 12 data points. A portion of the output is given below. Analysis of Variance Model Summary S R - sq R - sq (adj) ? 71.93% 55.89% Coefficients Regression Equation Y = -34 + 1.011 x1 + 4.85 x2 + 1.76 x3 - 0.253 x4 a) Fill in the missing values. (Write approximate values of P - values) b) Is the model overall significant at alpha = 0.05? c) Is x4 a significant variable for the model? d) Estimate true beta_1 with a 98% confidence interval. e) What is the proportion of variability in response explained by this regression model?

Explanation / Answer

a) Filled missing values are as follows:

Excel formula:

b) Yes overall model is significant at 5% level since p-value for F-stat<0.05

c) no, since p-value for this > 0.05

d) 98% CI for beta1:

excel formula:

e) 71.93% (R-sq) of the variability is explained by the model.

ANOVA Source DF Adj SS Adj MS Regression 4 4782.05 1195.513 S 16.23422 Coefficients Term Coef SE Coef t-value x1 1.011 0.37 2.732432

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