Question 1: Predict sales price of a 10 year old house with 1,500 square feet AN

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Question 1: Predict sales price of a 10 year old house with 1,500 square feet ANS: 209,380

Question 2: What is the estimated effect of a 1 year increase in age on sale price, given the house is 1,500 square ft ANS: 460 decrease in predicted sale price

Question 3: What is the estimated effect of 1 additional Square Ft on Sale Price , given the house is 1,500 Square Ft and 10 years old? ANS: 86.55 increase in predicted sale price

ANS = the answers for the problems need help with the work to solve them.

Regression Statistics Multiple R Square Adjusted R Square Standard Error Observations 0.779450725 0.607543433 0.607122342 58416.65152 3733 ANOVA MS 4.92351E+12 3412505175 df Significance F Regression Residual 4 3728 3732 1.9694E+13 1.27218E+13 3.24159E+13 1442.78508 0 Standard Error Coefficients 82468.77246 88.34253065 t Stat 11.07590142 14.65377872 0.38258211 P-value Lower 95% Upper 95% Intercept SquareFeet SqFtA2 0.00044696 392.1117586 0.045081189 7445.784261 6.028651882 0.001168271 83.37279246 0.040843685 4.4806E-28 2.57553E-47 0.702051447 2.65506E-06 0.269773146 67870.56392 76.5227526 0.002737472 555.5724994 0.12515934 97066.98101 100.1623087 0.001843553 228.6510178 0.034996962 -4.703114134 Age Sqt 1.10374929

Explanation / Answer

Question 1: Predict sales price of a 10 year old house with 1,500 square feet

From the coefficients columns, the regression equation is,

Sale Price = 82468.77246 + 88.34253065 * SquareFeet - 0.00044696 * Sqft^2 - 392.1117586 Age - 0.045081189 Age * Sqft

Given, Age = 10, Sqft = 1500

Sale Price = 82468.77246 + 88.34253065 * 1500 - 0.00044696 * 1500^2 - 392.1117586 * 10 - 0.045081189 * 10 * 1500 = 209379.6 = 209380 (rounded)

Question 2: What is the estimated effect of a 1 year increase in age on sale price, given the house is 1,500 square ft

When Sqft = 1500

Sale Price = 82468.77246 + 88.34253065 * 1500 - 0.00044696 * 1500^2 - 392.1117586 * Age - 0.045081189 * Age * 1500

Sale Price = 213976.9 - 459.7335 * Age

Now, Age becomes Age + 1 , then

Old Sale Price = 213976.9 - 459.7335 * Age

New Sale Price = 213976.9 - 459.7335 * (Age+ 1)

New Sale Price = 213976.9 - 459.7335 * Age - 459.7335

New Sale Price = Old Sale Price - 459.7335

Increase in Sale price = New Sale Price - Old Sale Price = - 459.7335 = - 460 (Rounded)

So, there is decrease of 460 in predicted sale price.

Question 3: What is the estimated effect of 1 additional Square Ft on Sale Price , given the house is 1,500 Square Ft and 10 years old?

Given, Age = 10, Sqft = 1500

Old Sale Price = 82468.77246 + 88.34253065 * 1500 - 0.00044696 * 1500^2 - 392.1117586 * 10 - 0.045081189 * 10 * 1500 = 209379.6

When Age = 10, Sqft = 1500 + 1 = 1501

New Sale Price = 82468.77246 + 88.34253065 * 1501 - 0.00044696 * 1501^2 - 392.1117586 * 10 - 0.045081189 * 10 * 1501 = 209466.1

Increase in Sale price = 209466.1 - 209379.55 = 86.55

So, there is increase of 86.55 in sale price.

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