In: Statistics and Probability
Evaluate the predictability of the model using explanatory language that someone who does not have experience with statistics or regression could understand to make informed business decisions, i.e., Interpret R2, F-test and t-tests.
X1 | X2 | Y |
194 | 1.6 | 728.4 |
2256 | 1846 | 30184 |
32.7 | 1.6 | 179.7 |
37 | 36 | 1937 |
227 | 66 | 3472 |
29 | 14.1 | 782.9 |
-14.7 | 14.1 | 295.5 |
549 | 420 | 10100 |
512.4 | 200 | 5954.3 |
1086 | 509 | 17373 |
180 | 93 | 5550 |
23.1 | 2.6 | 88.1 |
5.4 | 6 | 174.6 |
8.1 | 8.2 | 172.6 |
43.8 | 17.6 | 1868.3 |
130.1 | 115.4 | 1672.7 |
101.8 | 14.2 | 1311.7 |
200 | 1219 | 21641 |
33 | 16 | 374.2 |
The regression equation is defined as,
Now, the regression analysis is done in excel by following steps
Step 1: Write the data values in excel. The screenshot is shown below,
Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,
Step 3: Select Input Y Range: 'Hours' column, Input X Range: 'Feet and Large' column then OK. The screenshot is shown below,
The result is obtained. The screenshot is shown below,
a)
Intercept:
Coefficients of Independent variable:
R-square:
Significance F:
From the ANOVA table in regression output summary,
The regression equation is,
The profit for the firm is $3292.2634
Interpretation of R2, F-test and t-test
R-square: The R-square value determine how well the model fit the data values. The R-square value for the above model is 0.9426 which mean the model explains the 94.26% of the variance of the data values.
F-test: From the ANOVA table, the significance F value is 0.000 which is less than 0.05 at 5% significance level hence be can conclude that the model is overall significant which means the independent variables significantly fit the regression model.
t-test: The t-est in regression model is used to test the significance of the independent variables in the model.
For variable X1, the p-value for the t-test is 0.1376 which is greater than 0.05 at 5% significance level hence the variable X1 is not significant in the model.
For variable X2, the p-value for the t-test is 0.0000 which is less than 0.05 at 5% significance level hence the variable X2 is significant in the model.