Regression Analysis
Solve the following problem:
The data file contains information on 76 single-family homes in Eugene, Oregon during 2005. At the time the data were collected, the data submitter was preparing to place his house on the market and it was important to come up with a reasonable asking price. Whereas realtors use experience and local knowledge to subjectively value a house based on its characteristics (size, amenities, location, etc.) and the prices of similar houses nearby, regression analysis provides an alternative that more objectively models local house prices using these same data. Please address items (a) through (c) below
| id |
price |
size |
bath |
bed |
garage |
| 1 |
388 |
2.18 |
3 |
4 |
0 |
| 2 |
450 |
2.054 |
3 |
4 |
2 |
| 3 |
386 |
2.112 |
2 |
4 |
2 |
| 4 |
350 |
1.442 |
1 |
2 |
1 |
| 5 |
155.5 |
1.8 |
2 |
4 |
1 |
| 6 |
220 |
1.965 |
2 |
3 |
1 |
| 7 |
239.5 |
1.8 |
1.1 |
4 |
1 |
| 8 |
207 |
2.254 |
2 |
4 |
2 |
| 9 |
269.9 |
1.922 |
2.1 |
4 |
2 |
| 10 |
238.8 |
1.92 |
2.1 |
3 |
2 |
| 11 |
359.9 |
2.2 |
2 |
3 |
2 |
| 12 |
249.7 |
1.868 |
2 |
4 |
2 |
| 13 |
265 |
1.875 |
2.1 |
3 |
2 |
| 14 |
349 |
2 |
2 |
3 |
2 |
| 15 |
319 |
1.855 |
2 |
4 |
2 |
| 16 |
339 |
1.928 |
3 |
3 |
2 |
| 17 |
283 |
1.98 |
3 |
4 |
2 |
| 18 |
275 |
1.528 |
2.1 |
3 |
2 |
| 19 |
299.9 |
1.882 |
2.1 |
3 |
2 |
| 20 |
277 |
1.44 |
2 |
3 |
2 |
| 21 |
299 |
1.994 |
3 |
2 |
3 |
| 22 |
185 |
1.86 |
2 |
5 |
0 |
| 23 |
232 |
2.031 |
2 |
4 |
0 |
| 24 |
214.9 |
1.868 |
2 |
4 |
2 |
| 25 |
195 |
2.112 |
2 |
3 |
2 |
| 26 |
256 |
1.974 |
2 |
3 |
2 |
| 27 |
269.7 |
2.1 |
2 |
4 |
2 |
| 28 |
330 |
1.894 |
2 |
3 |
1 |
| 29 |
249.9 |
1.804 |
2 |
3 |
2 |
| 30 |
279.9 |
2.01 |
2 |
3 |
2 |
| 31 |
325 |
1.661 |
1.1 |
3 |
2 |
| 32 |
259.9 |
1.708 |
2 |
4 |
0 |
| 33 |
324.5 |
1.8 |
2.1 |
3 |
1 |
| 34 |
359.9 |
1.968 |
3 |
3 |
2 |
| 35 |
252.5 |
1.888 |
2 |
6 |
0 |
| 36 |
269 |
1.8 |
3 |
5 |
0 |
| 37 |
235 |
1.712 |
1 |
3 |
1 |
| 38 |
256.5 |
2.2 |
2.1 |
3 |
2 |
| 39 |
319.9 |
1.92 |
2.1 |
3 |
2 |
| 40 |
355 |
2.129 |
2 |
3 |
2 |
| 41 |
285 |
2.235 |
3.1 |
4 |
2 |
| 42 |
242 |
2.279 |
2.1 |
4 |
1 |
| 43 |
197 |
1.85 |
2 |
4 |
1 |
| 44 |
281.8 |
1.886 |
2 |
3 |
2 |
| 45 |
259 |
2.08 |
2 |
4 |
2 |
| 46 |
189.5 |
1.906 |
2.1 |
3 |
0 |
| 47 |
339.9 |
2.048 |
2 |
2 |
3 |
| 48 |
297 |
2.106 |
2.1 |
3 |
2 |
| 49 |
295 |
2.028 |
3 |
5 |
2 |
| 50 |
222.5 |
1.794 |
2 |
3 |
0 |
| 51 |
199 |
2.016 |
2 |
5 |
1 |
| 52 |
385.5 |
1.904 |
1.1 |
3 |
1 |
| 53 |
230 |
2.234 |
3 |
4 |
2 |
| 54 |
285 |
2.269 |
3.1 |
4 |
0 |
| 55 |
243 |
1.81 |
3 |
3 |
2 |
| 56 |
217 |
1.875 |
2 |
3 |
0 |
| 57 |
259.9 |
1.683 |
2.1 |
3 |
1 |
| 58 |
349.5 |
2.08 |
2.1 |
3 |
2 |
| 59 |
345 |
2.126 |
3.1 |
3 |
2 |
| 60 |
336 |
2.126 |
3.1 |
3 |
2 |
| 61 |
333.75 |
2.126 |
3.1 |
3 |
2 |
| 62 |
340 |
2.126 |
3.1 |
3 |
2 |
| 63 |
345 |
2.126 |
3.1 |
3 |
2 |
| 64 |
374.5 |
1.712 |
1.1 |
3 |
2 |
| 65 |
236.5 |
1.95 |
3 |
4 |
2 |
| 66 |
350 |
2.02 |
2 |
3 |
2 |
| 67 |
270 |
2.053 |
2.1 |
3 |
2 |
| 68 |
299 |
1.743 |
2 |
3 |
2 |
| 69 |
285 |
1.878 |
2.1 |
3 |
2 |
| 70 |
255 |
1.9 |
2 |
3 |
2 |
| 71 |
259 |
2.208 |
3 |
3 |
2 |
| 72 |
249.9 |
2.081 |
2.1 |
4 |
1 |
| 73 |
215 |
2.044 |
1.1 |
4 |
0 |
| 74 |
435 |
2.253 |
2 |
3 |
2 |
| 75 |
274.9 |
1.861 |
2 |
4 |
2 |
| 76 |
349.5 |
2.896 |
3 |
5 |
2 |
a) Using price as the dependent variable (Y) use regression to determine the fitted regression equation using size, bath, bed, and garage. (Use Data Analysis in Excel or MegaStat)
b) What does the R-squared value tell you?
c) Using an alpha value of 0.05, which variables are significant (size, bath, bed, garage)?
d) The variable "bed" has a negative coefficients. What does this mean. (i.e. what happens to the selling price when the number of bedrooms increases)