1) Below are data for 40 houses located in one of two neighborhoods (A or B).

Neighborhood Appraised Land Value Appraised Value of Improvements Sale Price Has a yard? (yes/no)

A 56658 53806 255000 no

A 93200 11121 422000 no

A 76125 78172 290000 no

A 28996 5864 305900 no

A 38000 72005 113000 no

A 30000 50765 93900 no

A 46651 8573 191500 no

A 45990 91402 184000 yes

A 42394 98181 168000 yes

A 47751 3351 169000 yes

A 63596 2182 208500 yes

A 51428 72451 264000 yes

A 54360 61934 237000 yes

A 65376 34458 286500 yes

A 42400 15046 202500 yes

A 40800 92606 168000 yes

A 12170 22786 375000 yes

A 24637 90598 169900 yes

A 30600 80858 135000 yes

A 44730 99047 176000 yes

B 38979 25946 140000 no

B 14861 59258 74900 no

B 14976 48957 57300 no

B 17006 54076 92000 no

B 18260 59267 82000 no

B 16680 55525 78000 no

B 53421 19792 175000 no

B 31417 99413 185000 no

B 32311 75343 123000 no

B 26817 78726 108000 no

B 24564 66533 108000 no

B 24564 71149 112900 no

B 27640 85347 106000 no

B 29656 78968 147500 no

B 13440 41177 61000 no

B 45765 81227 320000 yes

B 16680 72867 99500 yes

B 17020 61935 93000 yes

B 25751 82259 110000 yes

B 25751 64568 100500 yes

a) Give appropriate summary statistics (one measure of central tendency and one measure of variation) for each of the 3 variables Appraised Land Value, Appraised Value of Improvements, and Sale Price, calculated separately for neighborhoods A and B. Important: PROVIDE ONLY ONE (APPROPRIATE) CENTRAL TENDENCY MEASURE AND ONE (APPROPRIATE) MEASURE OF VARIATION FOR EACH VARIABLE FOR EACH NEIGHBORHOOD. [please put your answers in a table or you cut and paste into word. If you use Descriptive Statistics in the Data analysis Tool in Excel to calculate summary statistics, you shouldn't give the whole Excel output as you will end up providing too many measures of central tendency and variation.]

b) Based on this data sample, do neighborhoods A and B differ in the number of houses with and without yards? In your answer be sure to calculate an appropriate statistic, state the result of the test, and state your conclusion. (Paste your output from Excel for the statistical test that you do in your answer, as well as stating your conclusion and writing out the appropriate statistic that supports your conclusion.)

c) Based on this data sample, do houses in neighborhoods A and B have different sale prices? (In your answer be sure to calculate an appropriate statistic, state the result of the test and state your conclusion.) (Paste the output from Excel for the statistical test that you do in your answer, as well as stating your conclusion and writing out the appropriate statistic that supports your conclusion.)

d) Provide a correlation matrix (paste the output from Excel) for Appraised Land Value, Appraised Value of Improvements and Sale Price. In words, explain the meaning of the correlation between Sale price and Appraised Land Value and the meaning of the correlation between Appraised Land Value and Appraised Value of Improvements.

e) Imagine you are interested in the relationship between house Sale price and Appraised Land Value while controlling for any effects of Appraised Value of Improvements (use Sale price as the Y variable). Conduct a linear regression that allows you to test this relationship (using data for all the houses, i.e., from both neighborhoods). State your conclusion about the relationship, and provide the statistics that support your conclusion. (Paste your Excel output for this regression into your answer.)

f) Imagine you are interested in the relationship between house Sale price and Neighborhood, while controlling for any effects of Appraised Land Value and Appraised Value of Improvements on Sale price. Conduct a linear regression that allows you to test this relationship. State your conclusion about the relationship, and provide the statistics that support your conclusion. (Paste your Excel output for this regression into your answer.)

g) Looking at your answers to parts d, e, and f above, do you think you have any multicollinearity concerns for your two regressions? Why or why not?