6) Use the RailTrailsHouseValues.xlsx file described in problem 5 to predict pri

Question

6) Use the RailTrailsHouseValues.xlsx file described in problem 5 to predict price2014 using squarefeet as the independent variable.

a) What is the regression equation?

b) Interpret the coefficients of the regression equation.

c) Predict price2014 for a house with 1800 square feet.

d) House number 35 happens to have 1800 square feet but price2014 for this house is different from what you calculated in part c. Is this surprising? Why or why not?

e) What is the coefficient of determination and what does it tell you?

f) What is the standard error of the estimate?

g) Say you want to run a test to determine if the slope of the regression line is truly different from 0. Specify the test. What is the p-value for this test? Would you reject the null hypothesis at alpha= .01?

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

From Excel

a) The regression equation is

y=a+bx

from excel

The fitted regression equation is

y=43.77 +159.17 (Square feet)

b)

Intercept=43.77

and Slope=159.17

C)

Predict price2014 for a house with 1800 square feet.

when x=1800

now y=43.77 +159.17 (Square feet)

y=43.77 +159.17 (1800)

y=286549.77

e)

From excel

coefficient of determination = 0.643

f) standard error=66.61

SUMMARY OUTPUT Regression Statistics Multiple R 0.801669232 R Square 0.642673558 Adjusted R Square 0.639170357 Standard Error 66.61057414 Observations 104 ANOVA df SS MS F Significance F Regression 1 813976.3793 813976.4 183.4533 1.57E-24 Residual 102 452570.7959 4436.969 Total 103 1266547.175 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 43.77115824 19.53218673 2.240976 0.027195 5.029158 82.51316 5.029158 82.51316 squarefeet 159.1689474 11.75156264 13.54449 1.57E-24 135.8598 182.4781 135.8598 182.4781

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