MyKassels (MK) is a high-quality house builder and is looking for more rural sites to build exclusive estates, which will make them a profit. MK is not sure what is the best size of the site to look for and so is trying to establish if there is the relationship between the number of houses they have built on a site and the profit they have achieved. They have collected data on 20 of their sites over the last couple of years and the data is shown in the table below.

Site	Houses built	Profit (£Ks)
1	56	806
2	96	1204
3	28	411
4	94	1317
5	80	1195
6	97	1301
7	102	1363
8	94	1619
9	86	1432
10	45	836
11	91	1447
12	106	1405
13	96	1732
14	19	287
15	86	1232
16	96	1458
17	35	608
18	69	1079
19	82	1503
20	90	1255

In the following questions “Houses”means the variable representing the number of houses built on a site and “Profit” the profit in £Ks achieved on that site.

From the scenario description just given, would you expect any link between “Profit” and “Houses”, and, if so what?

Enter the data into SPSS and plot the dependent variable against the independent variable.

From this plot do “Profit” and “Houses” appear to be linked, and, if so , how?

Which sites, if any, appear of concern or interest?

In SPSS conduct a regression of the dependent variable against the independent variable toget a linear model linking these variables and then write this new model out:

What is the R-squared% value for this new model”? What is the value of the F statistic for this model”?

What is 5% critical value of the F distribution for this model?

Based on the model’s statistics:

How should we treat the null hypothesis that there is no model? How good is this model?

In simple words how much variability in the dependent variable is explained by the independent variable?

Now look at the residual plot.

Do the residuals appear random?

Are any sites extreme outlier(s) in residuals? and, if so, which sites? Do any sites have high leverage? and, if so, which sites?

MK is more interested in larger sites, in future, so re-examine the data using only those sites where they built more than 70 houses.

Remove all sites with 70 or less houses built and redo the regression and then write this new model out:

What is new R-squared% value for this new model? What isnew value of the F statistic for this new model?

What is 5% critical value of the F distribution for this new model?

Based on the new model’s statistics:

How should we treat the null hypothesis that there is no model?

How do the new a and b coefficients compare to those in the initial model? How good is this new model?

In simple words how much variability in the dependent variable is explained by the independent variable?

What can you conclude about the model for larger sites? and what would advise about using it?