The following Excel file AmesHousing. xlsx contains data on selling price (in thousands), age at time of sale, and total square footage for 2,930 houses in Ames, Iowa. An analyst wants to predict the sale price of a home using its total square footage. She chooses to fit the following model: 1 SalePrice 000s Age SF 215 105 172 244 189.9 195.5 213.5 191.5 236.5 189 175.9 185 180.4 49 52 42 1918 3087 4220 2803 2926 2676 2642 3600 12 18 15 17 18 12 20 2659 2859 2329 2833 16 212 538 164 394.432 141 210 18 19 20 2648 3825 1728 3964 3810 2346 59 32 170 216 149 149.9 142 126 115 36 10 23 25 26 27 28 29 30 2156 2197 39 42 39 1728 3013 1745 1617 1617 2193 2484 1702 2337 4201 96 105.5 39 39 39 35 36 37 38 127.5 149.9 120 146 376.162 nA 35 35 32
Use Excel's Data Analysis feature, fit this model (in Excel, go to Data -> Data Analysis -> Regression).
Using the test statistic you calculated earlier, what would be the conclusion of the test of the following hypotheses at the 0.05 level of significance?
That is, what would be the conclusion of the test that there is no linear relationship between the square footage of a house and its mean selling price at the 0.05 level of significance?
a) Reject the null hypothesis and conclude that there is a linear relationship between square footage and the selling price of a home.
b) Fail to reject the null hypothesis. We cannot conclude that at least one term is not equal to 0.
c) Reject the null hypothesis and conclude that there is not a linear relationship between square footage and the selling price of a home.
d) Fail to reject the null hypothesis and conclude that there is not enough evidence to conclude that a linear relationship exists between square footage and the selling price of a home.
e) Reject the null hypothesis and conclude that for each additional square foot, the mean selling price of a house increases by 71.8.
f) Fail to reject the null hypothesis. We cannot conclude that the true mean square footage of a house is different from 0.
g) Reject the null hypothesis and conclude that the mean selling price of a house is not 0.