ld Price ($ thousands) SqFt 1 153000 920 1 0 33 Yes Baths Bedrooms Garage Age of Property Lot Size Property Condition Basement Outdoor Amenities School Quality Crime Rate Proximity to Amenities Transportation Accessibility 3280 Poor Property Tax Rate None 6 1.83 3.5 No 186 2 163150 750 1 2 0 38 2772 Poor No None 9 2.34 3.9 Yes 104 3 164900 900 1 2 0 13 3530 Excellent Yes None 6 2.98 3.9 No 2.11 4 170175 1500 т 2 0 31 5561 Fair Yes Deck 7 2.49 4.8 No 184 5 176900 1030 2 2 0 47 3247 Excellent No None 3 2.82 4.3 No 1.95 6 187700 1090 2 0 36 3898 Pocr No Garden 8 2.68 4 No 15 7 295000 1280 2 2 1 45 4617 Excellent Yes None 9 2.66 5 No 2.22 8 251650 1365 1 2 1 24 4674 Good No Garden 8 2.69 3.8 No 2.32 9 472990 1690 3 3 1 15 6315 Fair Yes Deck g 1.2 4 No 15 10 473000 1765 3 3 1 29 6944 Fair Yes Deck 9 1.74 4.2 No 1.88 11 773650 2780 3.5 4 2 8 10913 Fair Yes Deck 8 1 1.6 No 1.63 674000 1910 3 3 2 5 6591 Poor Yes Garden 6 1 2.8 No 1.95 13 885000 1920 4 4 2 29 5977 Fair No Deck 7 1 1.8 No 2.19 14 780000 1930 4 4 2 47 7691 Good Yes Garden 8 1 2.1 Yes 23 15 385900 950 1.5 3 1 4 3647 Poor Yes Deck 6 1.94 4 No 134 16 284650 850 1 2 1 12 2656 Fair No None 5 1.94 3.7 No 1.09 17 189500 950 2 1 18 392800 1025 2 2 19 299600 1560 1.5 2 20 115350 980 1.5 1 21 120170 750 1.5 1 22 164900 840 1 1 23 574900 2180 2.5 3 24 970000 3400 3.5 4 25 810000 2790 3 4 26 840000 2860 3 4 27 185500 1350 1 1 28 289600 1100 1.5 2 OHHOOOHMNNOO 0 45 3725 Fair No None 7 2.93 4.1 Yes 1.93 1 2 3967 Excellent No Garden 6 1.65 3.6 No 1.66 1 27 5489 Excellent No Pool 7 1.77 3.8 Yes 197 0 31 3519 Fair No Deck 7 3.06 4 Yes 1.19 0 36 2549 Good No None 6 1.9 5 No 1.63 0 36 2566 Poor No None 6 2.7 5 Yes 15 1 26 7271 Good Yes Garden 6 1 3.3 No 2.27 3 43 12930 Fair Yes Garden 9 1 1.6 No 2.94 2 27 8383 Good Yes Garden 8 1 1.9 No 2.79 2 5 9534 Excellent No Deck 9 1 1.8 Yes 28 0 20 4588 Good Yes None 6 2.59 5 Yes 2.02 0 11 3891 Fair No Pool 6 1.07 4.5 No 1.93 29 389800 1250 2 3 1 10 4900 Fair Yes None 8 1.38 3.3 No 2.29 30 689500 1870 3 3 1 40 6258 Good Yes Garden 9 1.22 2.8 No 19 31 889100 2850 3.5 4 2 38 9539 Good Yes Garden 7 1 1.9 Yes 2.15 32 283700 985 1.5 2 33 160450 980 1 1 34 195989 1100 1.5 1 35 999900 3250 4 4 36 225340 1150 2 2 COONO 0 6 3681 Good No None 6 2.2 4.3 No 1.09 0 8 3383 Poor Yes None 8 1.79 4.7 No 2.08 0 23 3547 Fair No Garden 8 2.64 4.9 No 1.12 2 47 11220 Good No Garden 8 1 1.2 Yes 2.21 0 26 3612 Good No None 7 2.27 4.3 No 1.22 37 125750 950 1.5 1 0 46 3018 Good No Deck 6 3.19 3.7 No 2.14 38 124700 890 2 1 0 43 3114 Fair No None 3 2.24 4 No 2.18 39 200500 1200 2 2 1 12 4103 Fair Yes Deck 9 2.08 4.8 Yes 1.72 40 128500 980 1 1 0 26 3837 Poor Yes None 8 1.33 4.1 No 2.1 41 174360 1100 1.5 1 1 13 3699 Excellent No Garden 7 2.88 4 No 1.37 42 179800 1210 2 1 0 40 4333 Poor Yes Deck 7 2.56 4.4 Yes 2.15 43 205450 1350 2.5 2 1 18 4904 Fair Yes Garden 7 1.47 4.7 No 169 44 779800 2600 3 4 2 25 7834 Excellent Yes Garden 9 1 1.9 No 199 45 128800 985 1.5 1 0 33 3609 Fair No None 8 2.13 2.8 Yes 1.11 46 522200 2345 3 3 1 47 7452 Fair No Pool 6 1.66 2.8 Yes 1.77 47 1173200 3250 3.5 5 2 40 12873 Poor No Deck 9 1 1.7 No 1.59 48 1824200 3875 4 5 3 43 12201 Good Yes Garden 8 1 1 Yes 2.91 49 2475200 4560 5 6 3 12 15571 Good No Garden 8 1 1 No 3.78 50 3126200 5870 5.5 7 4 44 18111 Fair Yes Pool 9 1 1 No 2
You must use Excel to perform the regression analysis. Provide the answers under the space provided for each question. You must provide the Excel output for the question along with the answers. Round off the values on the output to three-five decimal places if appropriate.
Property Condition: Categories "Poor" and "Fair" will be grouped together. If the property condition is "Poor" or "Fair," the indicator variable will be encoded as 0. If the property condition is "Good" and "Excellent", the indicator variable will be grouped together and encoded as 1.
Basement: If the home has a basement, it will be encoded as 1; otherwise, it will be recoded as 0. Categories include "Yes" (recoded as 1) and "No" (recoded as 0).
Outdoor Amenities: You will create two groups: one for "Garden" and "Deck" together, and one for "Pool." "None" will serve as the baseline category.
If the home has a garden or deck, the indicator variable will be encoded as 1 in a new variable; otherwise, it will be recoded as 0. If the home has a pool, the indicator variable will be encoded as 1 in a separate variable; otherwise, it will be encoded as 0.
Transportation Accessibility: If transportation is accessible, it will be encoded as 1 (Yes); if not, it will be encoded as 0 (No).
As preliminary analysis conduct a simple linear regression analysis for each independent variable associated with internal factors, using house price as the dependent variable. Make sure to use the indicator variables for the categorical data. (Significance level of α = 0.05). For each regression:
This analysis will provide insight into each variable’s predictive power and its contribution to the variability in house price, help determine which variables should be further investigated or potentially excluded from future modeling.
Questions:
1. Report the p-value of the independent variable and indicate whether it is a significant predictor of house price (based on the p-value being less than 0.05). (4p)
2. Report the explained variability (R-squared value) for each variable, whether it is significant based on the p-value. (4p)
3. Identify and list any variables that are not significant predictors of house price (i.e., those with p-values greater than 0.05). (3p)
Perform a multiple regression analysis using all internal factors Square Footage (SqFt), Bedrooms, Bathrooms, Garage, Age of Property, Lot Size, Property Condition, Basement, and Outdoor Amenities (Deck/Garden or Pool) to predict house price.
After running the regression:
1. Report the p-values for each internal factor to determine their significance as predictors.(4p)
2. Interpret the coefficients to understand the relationship each internal factor has with house price. (4p)
3. Assess the overall model fit (e.g., R-squared value) to evaluate how well the internal factors collectively explain the variability in house price. Is the overall model statistically significant at .05 level of significance? (3p)
4. Write the regression equation by substituting each coefficient and independent variable ito the model. Then, use this equation to predict the price of a house with the following features: 4 bedroom, 2.5 bathroom, 2-car garage, 3000 square feet with a garden. (4p)
5. The impact of additional bedrooms might depend on the overall square footage. For example, in a smaller home, adding bedrooms could decrease other usable space, while in a larger home, more bedrooms may be an asset.
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