The North Valley Real Estate data reports information on homes on the market.

a. Let selling price be the dependent variable and size of the home the independent variable. Determine the regression equation. Estimate the selling price for a home with an area of 2,200 square feet. Determine the 95% confidence interval for all 2,200-square-foot homes and the 95% prediction interval for the selling price of a home with 2,200 square feet.

b. Let days-on-the-market be the dependent variable and price be the independent variable. Determine the regression equation. Estimate the days-on-the-market of a home that is priced at $300,000. Determine the 95% confidence interval of days on the market for homes with a mean price of $300,000, and the 95% prediction interval of days-on-the-market for a home priced at $300,000.

c. Can you conclude that the independent variables “days on the market” and “selling price” are positively correlated? Are the size of the home and the selling price positively correlated? Use the .05 significance level. Report the p-value of the test. Summarize your results in a brief report.

Data From North Valley Real Estate:

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Pool Garage (Yes is 1) Mortgage Default (Yes is 1) Record Agent Price Size Bedrooms Baths (Yes is 1) Days Township type Years FICO 1820 346150 3010 372360 3210 Peterson 310622 3330 496100 206424 Marty Rose 2 1.5 33 Foxed 2 824 36 Fixed 820 Carter 4 21 2 Fixed 18 819 25 26 3 Fixed 17 817 5 Carter 4510 4.5 13 4 Fixed 17 816 Peterson 294086 3440 228810 4 3 1 31 4 Fixed 19 813 Carter 2630 4 2.5 39 4 Adjustable 10 813 4470 4040 4380 5280 Peterson 388960 4420 335610 2970 276000 2300 2970 453913 3660 376146 3290 Peterson 694430 5900 251269 2050 547596 4920 214910 8 Isaacs 384420 3.5 26 2 Fixed 812 Peterson 416120 3.5 26 4 Fixed 810 10 Isaacs 487494 4 1 32 3 Fixed 6 808 11 Rose 448800 4 35 4 Fixed Adjustable Adjustable Fixxed Adjustable Fixed 806 12 3 50 9. 805 13 Marty Rose Rose Isaacs Carter 25 25 801 2 1.5 34 20 798 795 792 14 15 346421 4 1 17 10 16 4 1 12 18 17 5 3.5 28 2 Adjustable Adjustable 9. 792 1. 18 3.5 36 3 10 788 19 Rose 1 38 Fixed 16 786 20 Rose 4.5 37 Fixed Fixed 2 785 1950 1950 4680 2540 393557 3180 478675 4660 384020 4220 21 Marty 1.5 20 4 6. 784 22 Rose 188799 2 1.5 1 52 Fored Fixed Fixed Foxed Adjustable Adjustable Fixed 10 782 23 Carter Isaacs 459950 4 31 781 780 4 24 264160 2.5 40 18 25 Carter 4 1 54 1 20 776 26 Isaacs 3.5 26 6. 773 27 Carter Marty Isaacs 5 3.5 1 23 4 772 1 3600 274482 2990 167962 28 313200 4 31 19 772 29 3 2 1 37 3 Fixed 769 30 Marty 1920 2 1.5 31 Foxed 6. 769 34S 67