Perfect Properties have collected sales data from property salesin the northern suburbs of Cape Town for the past month. In thetable below you are supplied with the selling price (SP) of thehouse in Rand, the size of the plot in m2 (P) as well asthe size of the house, also in m2 (H). They areinterested in understanding which of these two factors influencethe selling price.
House | Selling price (SP) | Plot size in m2 (P) | House area in m2 (H) |
1 | R3 264 000 | 1012 | 118 |
2 | R4 054 000 | 1922 | 268 |
3 | R3 448 000 | 1214 | 179 |
4 | R3 718 000 | 2023 | 189 |
5 | R3 634 000 | 1619 | 294 |
6 | R3 914 000 | 1821 | 170 |
7 | R3 564 000 | 506 | 188 |
8 | R3 972 000 | 1113 | 181 |
9 | R4 288 000 | 2023 | 242 |
10 | R3 824 000 | 1720 | 190 |
11 | R3 218 000 | 708 | 189 |
12 | R3 556 000 | 1012 | 233 |
13 | R3 674 000 | 708 | 213 |
14 | R3 416 000 | 1012 | 151 |
15 | R3 292 000 | 607 | 262 |
16 | R3 198 000 | 1821 | 123 |
17 | R3 684 000 | 1214 | 255 |
18 | R3 436 000 | 911 | 277 |
19 | R3 696 000 | 1113 | 272 |
20 | R3 904 000 | 708 | 276 |
Use the data in the sheet named “Perfect” andanswer the following questions:
- Decide which linear regression model (with size of plot (P) orsize of house (H) or both as independent variable) is the bettermodel in explaining the behaviour of selling prices (SP) andmotivate your selection.
The remaining answers must be based onthe model that you have selected.
- What is the total variation in “Selling Price” that isexplained by the independent variable(s) that you haveselected?
- Is the overall regression model statistically significant? Testat the 5% level of significance using the model that you haveselected in a. For this test formulate the appropriate null andalternative hypothesis, determine the region of acceptance, use theappropriate test statistic and draw the statistical and managementconclusions.
- Write down the linear regression equation in algebraic formatusing SP for Selling price, P for plot size and H for the size ofthe house.
- Compute the expected Selling price for a house that stands on aplot of 1500 m2 and has a house that covers 245m2.
Compute the 95% confidence interval of the mean expense for ahouse that stands on a plot of 1500 m2 and has a housethat covers 245 m2.
