Homework Answers
| X | Y | XY | X² | Y² |
| 1148 | 154 | 176792 | 1317904 | 23716 |
| 1087 | 159.9 | 173811.3 | 1181569 | 25568.01 |
| 1142 | 169 | 192998 | 1304164 | 28561 |
| 1279 | 169.9 | 217302.1 | 1635841 | 28866.01 |
| 1331 | 170 | 226270 | 1771561 | 28900 |
| 1466 | 179.9 | 263733.4 | 2149156 | 32364.01 |
| 1344 | 180 | 241920 | 1806336 | 32400 |
| 1544 | 189 | 291816 | 2383936 | 35721 |
| 1494 | 189.9 | 283710.6 | 2232036 | 36062.01 |
| Ʃx = | 11835 |
| Ʃy = | 1561.6 |
| Ʃxy = | 2068353.4 |
| Ʃx² = | 15782503 |
| Ʃy² = | 272158.04 |
| Sample size, n = | 9 |
| x̅ = Ʃx/n = 11835/9 = | 1315 |
| y̅ = Ʃy/n = 1561.6/9 = | 173.5111111 |
| SSxx = Ʃx² - (Ʃx)²/n = 15782503 - (11835)²/9 = | 219478 |
| SSyy = Ʃy² - (Ʃy)²/n = 272158.04 - (1561.6)²/9 = | 1203.088889 |
| SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 2068353.4 - (11835)(1561.6)/9 = | 14849.4 |
a) Explanatory variable = Square footage
b) Scatter plot: Answer B.
c)
Correlation coefficient, r = SSxy/√(SSxx*SSyy) = 14849.4/√(219478*1203.08889) = 0.914
d)
Yes, there is a linear relation.
e)
Slope, b = SSxy/SSxx = 14849.4/219478 = 0.067657806
y-intercept, a = y̅ -b* x̅ = 173.51111 - (0.06766)*1315 = 84.54109589
Regression equation :
ŷ = 0.06766 x + 84.54
Answer D.
f)
For each square foot added to the area, the expected asking price of the house will increase by $67.66.
Answer A.
g)
No, it is not reasonable
h)
Predicted value of y at x = 1094
ŷ = 84.5411 + (0.0677) * 1094 = 158.5587
Residual = y - ŷ = 189.9 - 158.5587 = 31.3413
Above average
--
Yes, there may be some reason.
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