5) RailTrailsHouseValues.xlsx has a number of variables relating to a set of hou

Question

5) RailTrailsHouseValues.xlsx has a number of variables relating to a set of houses in two towns in Western Massachusetts. The worksheet Var Defs in this spreadsheet gives the variable definitions. We want to predict price2014, the Zillow estimated house price in 2014. The Zip variable is numeric but actually represents a category so an indicator variable has been created to represent this variable.

a) Before doing any calculations, which one variable do you think will be the best predictor of price2014? Explain your reasoning.

b) Use the correlation tool in the data analysis toolpac to calculate the correlations between each pair of variables. Based on these values, which one variable do you think will be the best predictor of price2014? Explain your reasoning.

c) Run a series of four simple linear regressions. In each of them use price2014 as the dependent variable. The independent variable should be, in turn, no_rooms, bedrooms, squarefeet and acre. Evaluate these four regression models and determine which single independent variable is the best predictor of price2014. Explain your reasoning. Are there any of these variables that show no real relationship to price2014?

housenum price2014 distance garage_spaces no_rooms squarefeet Zip (1062 = 1) no_full_baths no_half_baths bedrooms acre zip 1 210.729 2.4 2 5 0.966 1 1 0 3 0.28 1062 2 204.171 1.97 1 5 0.96 1 1 0 3 0.29 1062 3 338.662 0.043371212 2 7 1.725 1 2 1 3 0.36 1062 4 276.25 0.554734848 1 6 1.727 0 1 1 3 0.26 1060 5 169.173 0.596590909 0 6 1.576 1 1 0 4 0.31 1062 6 211.487 1.88 1 6 1.32 1 1 1 3 0.31 1062 7 311.456 0.444886364 0 6 1.202 0 1 0 3 0.08 1060 8 377.857 0.444886364 0 9 2.136 0 1 1 4 0.11 1060 9 227.681 1.93 0 7 1.918 1 2 0 5 0.31 1062 10 224.366 2.873030303 0 5 1.008 1 1 0 3 0.27 1062 11 218.785 0.756628788 0 5 1.296 1 2 0 3 0.27 1062 12 269.62 1.41 2 7 1.432 1 1 0 3 0.51 1062 13 447.842 1.42155303 0 8 2.04 0 2 0 4 0.23 1060 14 386.446 0.246780303 0 6 1.604 0 1 1 3 0.11 1060 15 528.114 0.396022727 0 9 2.278 0 2 0 4 0.15 1060 16 221.22 1.567234848 0 6 1.208 1 1 0 3 0.23 1062 17 320.206 1.676704545 0 7 1.744 1 2 0 5 0.23 1062 18 179.487 1.598674242 0 5 1.008 1 1 0 3 0.23 1062 19 243.639 0.103030303 0 8 1.922 0 1 1 4 0.31 1060 20 325.666 0.3375 0 8 2.1 0 2 0 4 0.07 1060 21 282.765 1 1 7 1.664 1 2 0 4 0.23 1062 22 198.686 0.042045455 1 5 0.892 1 1 0 2 0.17 1062 23 168.761 2.15 0 5 1.01 1 1 0 3 0.33 1062 24 200.871 2.621401515 0 6 1.248 1 1 1 3 0.33 1062 25 237.206 2.579734848 1 6 1.3 1 2 0 3 0.31 1062 26 205.77 2.7 1 5 1.04 1 1 0 3 0.34 1062 27 287.489 0.216738636 0 8 1.466 0 1 0 4 0.13 1060 28 223.067 1.91 1 6 1.636 1 1 0 3 0.23 1062 29 237.594 0.708522727 1 7 1.335 1 1 0 4 0.21 1062 30 275.218 2.011742424 0 6 1.512 1 2 0 4 0.14 1062 31 280.283 1.991666667 1 8 1.752 1 2 0 4 0.21 1062 32 237.789 0.892045455 0 8 1.912 0 1 0 3 0.14 1060 33 191.694 0.875378788 0 5 0.942 1 1 0 3 0.26 1062 34 365.506 0.329545455 0 8 1.675 0 2 0 3 0.56 1060 35 474.245 0.326515152 1 7 1.8 0 2 0 4 0.11 1060 36 259.48 0.704356061 0 6 1.412 1 2 0 3 0.32 1062 37 326.891 0.866856061 2 7 1.763 1 2 0 3 0.5 1062 38 228.829 0.204734848 2 7 1.796 0 2 0 4 0.34 1060 39 426.5 0.138825758 2 7 2.224 0 2 0 4 0.19 1060 40 350.766 1.145454545 0 6 1.602 0 1 0 3 0.11 1060 41 279.187 0.179545455 1 9 1.9 1 2 0 4 0.28 1062 42 214.737 2.28 0 6 1.348 0 1 0 3 0.1 1060 43 212.959 2.28 0 5 1.084 0 1 0 2 0.1 1060 44 301.366 0.421969697 0 4 1.83 0 1 1 2 0.1 1060 45 144.366 2.28 0 4 0.587 0 1 0 2 0.1 1060 46 318.348 2.28 0 6 1.389 0 2 0 3 0.1 1060 47 185.141 2.28 0 4 0.645 0 1 0 1 0.1 1060 48 132.135 2.28 0 4 0.804 0 1 0 1 0.1 1060 49 200.219 2.28 0 5 0.8 0 1 0 2 0.1 1060 50 525.112 1.21 2 8 3.07 1 3 0 5 0.26 1062 51 210.701 2.53 2 5 0.864 1 1 1 3 0.35 1062 52 185.508 3.48 0 5 0.864 1 1 0 3 0.46 1062 53 209.945 2.4 0 6 1.008 1 1 0 4 0.43 1062 54 142.702 0.126893939 0 4 0.524 0 1 0 1 0.28 1060 55 367.384 0.73219697 0 7 1.856 1 1 1 2 0.55 1062 56 201.443 0.935037879 0 5 0.96 1 1 0 3 0.28 1062 57 360.87 0.390530303 2 9 2.542 1 1 1 4 0.55 1062 58 313.64 0.285795455 1 8 1.395 1 1 0 3 0.18 1062 59 270.622 0.203598485 1 7 1.349 1 2 0 3 0.26 1062 60 258.091 0.502462121 0 6 1.3 1 1 1 2 0.25 1062 61 357.303 0.096780303 2 8 2.256 1 1 1 4 0.22 1062 62 289.946 0.115340909 2 5 1.519 1 1 0 2 0.31 1062 63 296.142 0.385984848 2 7 1.454 1 1 0 3 0.26 1062 64 331.387 0.75625 1 6 1.584 1 1 1 3 0.19 1062 65 389.242 0.6375 2 7 1.624 0 1 0 4 0.14 1060 66 495.218 0.111363636 2 11 2.85 0 3 0 6 0.24 1060 67 246.02 0.300568182 1 7 1.376 1 1 0 3 0.37 1062 68 212.892 1.58 1 7 1.427 1 1 0 3 0.28 1062 69 384.14 0.166098485 1 8 1.837 0 1 1 3 0.23 1060 70 295.182 0.192045455 0 7 1.386 0 1 0 3 0.16 1060 71 520.147 0.35530303 2 6 1.966 0 2 1 3 0.2 1060 72 284.484 0.165719697 0 6 1.376 0 1 0 3 0.12 1060 73 228.565 1.72 0 6 1.2 0 2 0 3 0.33 1060 74 447.27 0.911363636 2 8 1.734 1 2 0 3 0.33 1062 75 286.163 0.785227273 0 7 1.556 1 2 0 3 0.36 1062 76 222.864 0.985984848 0 6 1.7 1 2 0 3 0.38 1062 77 310.018 0.35719697 1 7 2.042 0 2 0 4 0.18 1060 78 211.725 1.871780303 1 6 1.32 1 1 1 3 0.39 1062 79 266.124 2.89 2 7 1.728 1 1 0 3 0.46 1062 80 214.289 2.94280303 1 6 1.294 1 1 0 3 0.27 1062 81 211.104 1.589962121 1 5 0.966 1 1 0 3 0.51 1062 82 216.992 1.939962121 0 4 1.008 1 1 0 2 0.54 1062 83 202.485 2.577083333 2 7 1.594 1 1 1 3 0.35 1062 84 429.368 0.200189394 1 9 1.817 1 1 1 4 0.22 1062 85 208.703 1.75 0 5 0.96 1 1 0 3 0.28 1062 86 249.413 0.154356061 1 7 1.344 0 1 0 4 0.18 1060 87 332.674 0.385984848 2 7 1.5 1 2 0 4 0.17 1062 88 356.265 0.381818182 2 8 2.448 0 1 0 5 0.15 1060 89 513.096 0.624431818 2 14 4.03 0 3 1 5 0.35 1060 90 236.498 1.891060606 1 7 1.638 1 2 0 4 0.25 1062 91 295.772 1.887272727 1 7 1.772 1 2 0 4 0.43 1062 92 421.46 0.416477273 4 5 2.137 0 2 0 2 0.09 1060 93 233.023 0.038825758 0 4 0.934 0 2 0 2 0.05 1060 94 279.814 0.144507576 2 5 1.457 1 1 1 3 0.22 1062 95 347.408 0.153219697 1 7 1.737 1 4 0 4 0.25 1062 96 267.29 0.258712121 1 6 1.262 0 1 0 3 0.12 1060 97 879.328 0.458143939 1 12 3.175 0 3 0 6 0.26 1060 98 191.407 3.976780303 0 6 1.041 1 2 0 2 0.23 1062 99 467.861 0.674810606 0 9 2.102 0 2 1 3 0.19 1060 100 301.94 0.950568182 0 8 1.859 0 2 0 3 0.13 1060 101 534.865 0.764204545 2 9 2.528 0 2 1 4 0.46 1060 102 331.84 0.125189394 0 8 1.96 1 2 0 4 0.4 1062 103 320.805 1.070265152 0 8 1.941 0 1 0 4 0.2 1060 104 176.502 0.723295455 0 5 1.197 1 1 0 2 0.31 1062

Explanation / Answer

(a) squarefeet will be best predictor of price2014

(b) first row of each variale is correlation coefficient and next row is p-value of t-test of correlation coefficient.

from the table it can be seen that correlation between price2014 and squarefeet is highest and it is 0.80167. so squarefeet is best predictor for price2014.

answer d) all the four variable is regressed with price2014 seperately one bye one and it is found that square feet is best predictor because in this case modle R-square, adusted-R-sq is highest and Root MSE is minimum and its regression coefficient is significant as its p-value is less than 0.0001.

Acre is the variable among four variables that show no real relationship to price2014 as its regression coefficent is not significant at alpha=0.05

when price2014 is regressed with no_rooms

when price2014 is regressed with bedrooms

when price2014 is regressed with squarefeet

price2014 is regressed with acre

Correlation Coefficients price2014 distance garage_spaces no_rooms squarefeet Zip no_full_baths no_half_baths bedrooms acre price2014 1.00000 -0.44926 <.0001 0.34533 0.0003 0.71963 <.0001 0.80167 <.0001 -0.34850 0.0003 0.54771 <.0001 0.21512 0.0283 0.55985 <.0001 -0.06644 0.5028 distance -0.44926 <.0001 1.00000 -0.19493 0.0474 -0.37041 0.0001 -0.42342 <.0001 0.30701 0.0015 -0.19122 0.0518 -0.17159 0.0816 -0.22847 0.0197 0.17499 0.0756 garage_spaces 0.34533 0.0003 -0.19493 0.0474 1.00000 0.25840 0.0081 0.39415 <.0001 0.12852 0.1935 0.18613 0.0585 0.17580 0.0742 0.23726 0.0153 0.17966 0.0680 no_rooms 0.71963 <.0001 -0.37041 0.0001 0.25840 0.0081 1.00000 0.85579 <.0001 -0.19452 0.0479 0.48784 <.0001 0.19324 0.0494 0.74101 <.0001 0.10131 0.3062 squarefeet 0.80167 <.0001 -0.42342 <.0001 0.39415 <.0001 0.85579 <.0001 1.00000 -0.25225 0.0098 0.56366 <.0001 0.27251 0.0051 0.70304 <.0001 0.05255 0.5962 Zip -0.34850 0.0003 0.30701 0.0015 0.12852 0.1935 -0.19452 0.0479 -0.25225 0.0098 1.00000 -0.08107 0.4133 -0.02307 0.8162 -0.02692 0.7862 0.53391 <.0001 no_full_baths 0.54771 <.0001 -0.19122 0.0518 0.18613 0.0585 0.48784 <.0001 0.56366 <.0001 -0.08107 0.4133 1.00000 -0.16465 0.0949 0.48452 <.0001 0.02854 0.7737 no_half_baths 0.21512 0.0283 -0.17159 0.0816 0.17580 0.0742 0.19324 0.0494 0.27251 0.0051 -0.02307 0.8162 -0.16465 0.0949 1.00000 -0.01916 0.8469 0.13207 0.1814 bedrooms 0.55985 <.0001 -0.22847 0.0197 0.23726 0.0153 0.74101 <.0001 0.70304 <.0001 -0.02692 0.7862 0.48452 <.0001 -0.01916 0.8469 1.00000 0.05675 0.5672 acre -0.06644 0.5028 0.17499 0.0756 0.17966 0.0680 0.10131 0.3062 0.05255 0.5962 0.53391 <.0001 0.02854 0.7737 0.13207 0.1814 0.05675 0.5672 1.00000

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