Question

The following models are the results of fitting dependent variable, Y on five independents variables X1, X2, X3, X4 and X5. The following data represent a regression output from the Minitab software.

Comment on the significance of the model based on the statistics given. Hence, suggest the appropriate steps to obtain the best forecast model, and state the criteria (s) should be fulfill.

The regression equation is

Y = 19.3 + 4.607 X1 -- 0.725 X2 + 1.164 X3 + 3.0808 X4 -- 1.067 X5

Predictor	Coef	StDev	T	P	VIF
Constant	19.297	4.045	9.71	0.000
X1	4.607	0.005325	0.87	0.048	2.7
X2	-0.7253	0.1773	-3.53	0.002	8.9
X3	1.16375	0.06934	2.36	0.045	9.1
X4	3.08077	0.05551	1.46	0.267	19.8
X5	-1.66667	0.07565	-1.67	0.515	35.1

S = 2.125       R-Sq = 95.2%     R-Sq(adj) = 90.6%

Analysis of Variance

Source	DF	SS	MS	F	P
Regression	5	987.91	197.58	18.84	0.000
Error	23	241.32	10.49
Total	28	1229.23

Durbin-Watson statistic = 1.57

Source       DF      Seq SS

X1            1      789.69

X2            1      381.31

X3            1       29.95

X4            1       18.71

X5            1        9.57

Answer 1

The hypothesis being tested is:

H₀: β₁ = β₂ = β₃ = β₄ = β₅ = 0

H₁: At least one β_i ≠ 0

The test statistic is 18.84.

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

The best model would contain the following independent variables:

X1, X2, and X3

The criteria are:

Linearity must be assumed; the model should be linear in nature. Normality must be assumed in multiple regression. This means that in multiple regression, variables must have a normal distribution. Homoscedasticity must be assumed; the variance is constant across all levels of the predicted variable.