Question

0 Regression Statistics 1 Multiple R 2 R Square 3 Adjusted RS 0.853658537 0,97530483 0.951219512 4 Standard Err 0.191273014 5 Observation 6 7 ANOVA Significance F 0.220863052 df SS MS 0.713414634 0.356707 9 Regression 0 Residual 1 Total 2. 9.75 1 0.036585366 0.036585 0.75 2 Lower 95 % 3 Coefficients Upper 95% Lower 95.0% Standard Error t Stat P-value Upper 95.0% 4 Intercept 3.146341463 0.790522384 3.980079 0.156708 -6.898197794 13.19088072 -6.89819779 13.19088072 0.362905921-1.78102 0.325702 5 House -0.646341463 -5.257498391 3.964815464 -5.25749839 3.964815464 6 Sq ft 0,024390244. 0.009089707 2.683282 0.227104 -0,091105437 0.139885925 -0.09110544 0.139885925

1.Based on the table above, how to intepret this regression analysis?
2. When we need to look at the adjusted r2 and why?
3. How to conduct the hypothesis test?

Answer 1

1. In this case, the coefficients are the things to focus..

The Regression equation is given as Y = 3.14634 + -0.6463*House + 0.02439*Sqft

The house seems to have negative impact on the Dependent. In this case, even though the t stat is higher, the P value, which represents the significance levels seems to be on the higher side

Sqft seems to have positive impact on the Dependent . In this case, even though the t stat is higher, the P value, which represents the confidence levels seems to be on the lower side.

We see that the R² is on higher side, which means most of the variation of the Dependent is explained by the variables , House and Sqft.  But, we also need to consider that there are only 4 observations and one of these observations may have skewed the R² sharply. Therefore, we need more observations to understand and establish the relationship between these variables and Dependent.

2. Adjusted R² is a modified version of R² that has been adjusted for number of variables in a model. It checks the need of the variables to explain the Dependents. It increases only if the variables improves the regression model more than that expected by a chance. Adjusted R² is usually less than R² .

Adjusted R² is used to check the need of inclusion of a new variable in the model. Generally , if the new variable/ predictor improves the Adjusted R² , it is kept in the regression model .

3. The Null Hypothesis is generally something , which is inherently true . When we feel that the truth is something else and we have data to back it up, it is called Alternate Hypothesis.

The Null Hypothesis in this case , is there is no statistical significance that there is a relationship between variables( independent) and Dependents. The Alternate Hypothesis is that, there is statistical significance that there is a relationship between variables( independent) and Dependents. Now , we do the test to check , if there is any statistical significance or not accordingly establish the relationship.