Question

Build the regression model based on the outputs presented in the following tables Interpret the results of the regression analysis presented in the following tables Should the constant term be included in the regression model? R adjusted R Std. Error of the estimate del R Change in statistics R change Fchange Sig. F Durbin- change Watson 2.550 1 .675 455 331 61.3419 .519 99.587 Model Unstandardized Standardized Sig 95% Confidence Interval for B Lower bound bound Coefficients Coefficients Beta Upper Std. Error S 127 1.259 6.338 0.105 Constant 5.815 2.981 0.091 0.005 3.367 0.329 1.475 051 0002.820 040 -0.082 057 231 319 x1 x2 x3 3.915 4.182 0.879 2.116

Answer 1

Answer:

1. Regression model based on given output:

Y= 5.185 + 0.091*(x1) + 3.367 * (x2) + 2.116 (x3)

2. As per given table we have Correlation coefficient value R2 = 0.675 which is not too close to 1 or -1.

Hence linear relationship between the dependent and independent variables is considerable but not perfect correlation.

Also we consider correlation coff. of Adjusted R-square when we have more than 1 independent variable.

Here also we have 3 independent variables so we consider R-square adjusted = 0.331 which also negligible linear relationship.

As per table F test statistic value has value =0.000 which less that Alpha=0.05 (standard l.o.s) which shows that we reject the null hypothesis that this model is not significant.

Since P-value is less than alpha here we can use this model to predict the response variable.

3. Also from Coefficient table we can create the model (as specified in answer of 1. )

We can check of significance of each coefficient by comparing sig. value of table with Alpha=0.05 (standard)

a. For B1 of x1 variable: P-value is 0.051 which shows P-value >= Alpha 0.05 means we can consider this coefficient is not much significant in provided model.

b. For B2 of x2 variable: P-value is 0.000 which means P-value < Alpha so we reject null hypothesis that no relationship between x2 and Y. So it shows there is linear relationship which is considerable between x2 and Y.

Therefore it seems x2 plays significant role in regression model.

c. For B3 of x3 variable: P-value is 0.040 which means P-value < Alpha so we reject null hypothesis that no relationship between X3 and Y. So it shows there is linear relationship which is considerable between x3 and Y.

Therefore it seems x2 plays significant role in regression model.