There are numerous variables that are believed to be predictors of housing price

Question

There are numerous variables that are believed to be predictors of housing prices, including living area (square feet), number of bedrooms, and number of bathrooms. The data in the Case Study No. 2.xlsx file pertains to a random sample of houses located in a particular geographic area.

Develop the following simple linear regression models to predict the sale price of a house. Write the regression equation for each model.

Sale price based upon square feet of living area.

Sale price based upon number of bedrooms.

Sale price based upon number of bathrooms.

Develop the following multiple linear regression models to predict the sale price of a house. Write the regression equation for each model.

Sale price based upon square feet of living area and number of bedrooms.

Sale price based upon square feet of living area and number of bathrooms.

Sale price based upon number of bedrooms and number of bathrooms.

Sale price based upon square feet of living area, number of bedrooms, and number of bathrooms.

Discuss the joint statistical significance of each of the preceding simple and multiple linear regression models at a 90% level of confidence and 95% level of confidence.

Discuss the individual statistical significance of the coefficient for each independent variable for each of the preceding simple and multiple linear regression models at a 90% level of confidence and 95% level of confidence.

Compare any of the preceding simple and multiple linear regression models that were found to be jointly and individually statistically significant at a 90% level of confidence and select the preferred regression model. Explain your selection using the appropriate regression statistics.

Interpret the coefficient for each independent variable (or variables) associated with your selected preferred regression model.

Using the preferred regression model, predict the sale price of a house with the following values for the independent variables: 3,000 square feet of living area, 3 bedrooms, and 2.5 bathrooms. (Hint: You should only use the values for those independent variables that are specifically associated with your selected preferred regression model.)

Prepare a single Microsoft Excel file to document your regression analyses. Prepare a single Microsoft Word document that outlines your responses for each portion of the case study.

Selling Price Living Area (Sq FeetNo. Bathrooms No Bedrooms $145,000 $103,000 4$210,000 $559,000 $218,000 $262,138 $125,000 $130,000 0 $157,500 1 $193,000 2 $275,000 3 $240,000 4$200,136 5 $395,000 6 $366,703 7 $103,150 8 $310,000 9 $142,900 0 $359,770 1 $126,000 2 $760,000 3 $282,500 4$132,000 5 $325,000 6 $207,000 7 $155,000 8 $330,000 9 $101,760 0 $496,000 1$185,000 1,152 1,290 2,396 3,090 1,428 1,631 1,368 1,134 1,697 1,666 1,738 1,457 1,632 2,186 2,117 936 3,347 1,824 2,592 1,080 3,148 2,128 1,616 3,313 2,327 1,640 1,421 1,280 3,467 1,250 1.5 1.5 4 2.5 1.5 2.5 2.5 1.5 2.5 2.5 2.5 2.5 2.5 4 3.5 1.5 1.5 2.5 1.5 1.5 1.5 4 2.5 1.5

Explanation / Answer

The following are the individual and combined models: -

LA:

BedRooms

Bathrooms

LA_Bedrooms

Bedrooms_Bathrooms

LA_Bathrooms

All three variables

The model with all the three variables is the best out of all as p-values of all the independent variables is less than 0.05.

Predicted Value=9167.80+113.84*LA-30595.18*BD+60904.19*BR

=411149.55

SUMMARY OUTPUT Regression Statistics Multiple R 0.80 R Square 0.64 Adjusted R Square 0.64 Standard Error 77679.85 Observations 90 ANOVA df SS MS F Significance F Regression 1 944149872443.01 944149872443.01 156.47 0.00 Residual 88 531006059462.59 6034159766.62 Total 89 1475155931905.60 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept -23135.75 23780.97 -0.97 0.33 -70395.43 24123.93 -62668.14 16396.64 Living Area 145.17 11.61 12.51 0.00 122.11 168.23 125.88 164.46

BedRooms

SUMMARY OUTPUT Regression Statistics Multiple R 0.33 R Square 0.11 Adjusted R Square 0.10 Standard Error 122012.66 Observations 90 ANOVA df SS MS F Significance F Regression 1 165092185441.20 165092185441.20 11.09 0.00 Residual 88 1310063746464.40 14887088028.00 Total 89 1475155931905.60 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept 67471.24 58098.10 1.16 0.25 -47986.52 182929.01 -29108.37 164050.85 No. Bedrooms 60644.84 18211.07 3.33 0.00 24454.16 96835.51 30371.59 90918.08

Bathrooms

SUMMARY OUTPUT Regression Statistics Multiple R 0.76 R Square 0.58 Adjusted R Square 0.58 Standard Error 83900.98 Observations 90 ANOVA df SS MS F Significance F Regression 1 855691034143.36 855691034143.36 121.56 0.00 Residual 88 619464897762.24 7039373838.21 Total 89 1475155931905.60 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept -4634.10 25251.99 -0.18 0.85 -54817.13 45548.92 -46611.85 37343.64 No. Bathrooms 128956.24 11696.36 11.03 0.00 105712.17 152200.30 109512.74 148399.74

LA_Bedrooms

SUMMARY OUTPUT Regression Statistics Multiple R 0.81 R Square 0.66 Adjusted R Square 0.65 Standard Error 75631.40 Observations 90 ANOVA df SS MS F Significance F Regression 2 977506532642.66 488753266321.33 85.44 0.00 Residual 87 497649399262.94 5720108037.51 Total 89 1475155931905.60 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept 43648.15 36068.43 1.21 0.23 -28041.76 115338.05 -16317.68 103613.97 Living Area 164.21 13.78 11.92 0.00 136.82 191.60 141.30 187.12 No. Bedrooms -33241.74 13765.58 -2.41 0.02 -60602.33 -5881.16 -56127.81 -10355.67

Bedrooms_Bathrooms

SUMMARY OUTPUT Regression Statistics Multiple R 0.76 R Square 0.58 Adjusted R Square 0.57 Standard Error 84280.77 Observations 90 ANOVA df SS MS F Significance F Regression 2 857173327725.81 428586663862.91 60.34 0.00 Residual 87 617982604179.79 7103248323.91 Total 89 1475155931905.60 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept -19398.01 41085.16 -0.47 0.64 -101059.22 62263.19 -87704.45 48908.42 No. Bathrooms 126605.99 12826.38 9.87 0.00 101112.16 152099.81 105281.39 147930.59 No. Bedrooms 6273.21 13732.54 0.46 0.65 -21021.71 33568.12 -16557.93 29104.35

LA_Bathrooms

SUMMARY OUTPUT Regression Statistics Multiple R 0.84 R Square 0.70 Adjusted R Square 0.69 Standard Error 71288.37 Observations 90 ANOVA df SS MS F Significance F Regression 2 1033019138661.35 516509569330.68 101.63 0.00 Residual 87 442136793244.25 5082032106.26 Total 89 1475155931905.60 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept -53148.59 22974.12 -2.31 0.02 -98812.13 -7485.04 -91344.37 -14952.80 Living Area 94.89 16.06 5.91 0.00 62.96 126.81 68.18 121.59 No. Bathrooms 62678.32 14988.57 4.18 0.00 32886.91 92469.73 37758.96 87597.68

All three variables

SUMMARY OUTPUT Regression Statistics Multiple R 0.85 R Square 0.72 Adjusted R Square 0.71 Standard Error 69378.58 Observations 90 ANOVA df SS MS F Significance F Regression 3 1061204614951.42 353734871650.47 73.49 0.00 Residual 86 413951316954.18 4813387406.44 Total 89 1475155931905.60 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0% Intercept 9167.80 34104.06 0.27 0.79 -58628.83 76964.42 -47539.25 65874.85 Living Area 113.84 17.48 6.51 0.00 79.08 148.59 84.76 142.91 No. Bedrooms -30595.18 12643.45 -2.42 0.02 -55729.54 -5460.83 -51618.28 -9572.08 No. Bathrooms 60904.19 14605.45 4.17 0.00 31869.52 89938.86 36618.76 85189.62

The model with all the three variables is the best out of all as p-values of all the independent variables is less than 0.05.

Predicted Value=9167.80+113.84*LA-30595.18*BD+60904.19*BR

=411149.55

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