Regression Analysis Discussion
In regression analysis, a regression equation is modeled and then used for predicting the dependent variable. This discussion analyses the way the factor of the square footage of a house determines the total cost of building the house. It uses Excel to generate an output that is used to form the regression equation model (Gunst & Mason, 2018). From the data values of the independent variable (square footage) and the data values of the dependent variable (total cost), a regression analysis was performed in Excel and the regression output is as follows:
SUMMARY OUTPUT 

Regression Statistics 

Multiple R 
0.493824 

R Square 
0.243862 

Adjusted R Square 
0.149345 

Standard Error 
403.8854 

Observations 
10 

ANOVA 

df 
SS 
MS 
F 
Significance F 

Regression 
1 
420871.8 
420871.8 
2.580082 
0.146883 

Residual 
8 
1304987 
163123.4 

Total 
9 
1725859 

Coefficients 
Standard Error 
t Stat 
Pvalue 
Lower 95% 
Upper 95% 
Lower 95.0% 
Upper 95.0% 

Intercept 
558.323 
558.1674 
1.000279 
0.346467 
728.813 
1845.459 
728.813 
1845.459 
Square Footage 
0.452169 
0.281504 
1.606263 
0.146883 
0.19698 
1.101318 
0.19698 
1.101318 
The regression equation is derived from the coefficients shown in the regression output (colored yellow). Consequently, the regression equation will be t=0.4522s+558.323 where t is the total cost and s is the square footage. This equation can be used to predict the total cost of given square footage by just inserting the square footage in the equation. In this problem, the regression equation needs to be used to predict the total cost of a home that is measuring 1000 square feet. Inserting 1000 square feet into the equation, the result becomes t=(0.4522*1000)+558.323=1010.52
The strength of the regression analysis is the value of R^2 (adj) is used to tell the percent of the total variability that the regression model accounts for (Gunst & Mason, 2018). In the regression model, R^2 (adj) is 0.1493. This means that the regression model accounts for 14.93% of the total variability. This is a very low percentage. Based on this weak strength of the relationship between square footage and the total cost, it will be expected that this model will not give a valid prediction of the total cost. Using the linear regression model, it would not be appropriate to predict total cost if a complex wanted to list luxury apartments. This is because there are other predictor variables that need to be included in the regression model. A multiple regression model would give a better prediction of the total cost. Luxury apartments will for instance require such variables as a number of bedrooms and number of bathrooms to be factored in the regression model. By extending the simple linear regression to include more than one predictor variable, the resulting multiple regression model is more accurate and can give valid predictions or forecasting. Therefore, a more robust model would have been obtained by increasing the number of independent or predictor variables to make the model accounts for a greater percentage of total variability between the response variable and the independent variable or variables (Yao & Liu, 2018).
References:
Gunst, R. F., & Mason, R. L. (2018). Regression analysis and its application: a dataoriented approach. CRC Press.
Yao, K., & Liu, B. (2018). Uncertain regression analysis: an approach for imprecise observations. Soft Computing, 22(17), 55795582.
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