Use the following output for Questions 1 - 5. A realtor built a regression model

Question

Use the following output for Questions 1 - 5. A realtor built a regression model to explain the selling price of homes in a large Midwestern 2. city. The variables are PRICE-The sales price is measured in thousands of dollars. For example, a value of home that sold for $269,000 will have a value of 269 in this dataset. SOFT-The size of the living area in the house measured in thousands of square feet. For example, a home with 2,250 square feet will have a value of 2.25 in the dataset. BATH-The number of bathrooms. ACREAGE- The size of the lots measured in acres. The regression output is shown below: Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.919 0.844 0.834 32.5 Question 1 ANOVA Significance sS MS Regression Residual Total 262252.2 87417.4 82.90 1.42053E-18 46 Question 2 49 310756.8 1054.4 Upper 95% Standara Coefficients 11.37 44.58 24.34 25.65 P-value 16.30 0.70 0.4887 6.19 7.20 0.0000 8.40 2.90 0.0057 7.52 0.0000 Error :Stat Lower 95% Intercept sqft bath acreage 21.43 32.12 7.43 18.78 44.17 57.05 41.25 32.52 Lower 95.0% -21.43 32.12 7.43 18.78 3.41

Explanation / Answer

Answer

(1) Number of observation = total degree of freedom +1 = 49+1 = 50

so, there are 50 observations

(2) we know that total sum of squares = Regression sum of square + residual sum of squares

we have to find the residual sum of squares

setting the value of total sum of square and regression sum of square from the table, we get

310756.8 = 262252.2 + Residual sum of squares

subtracting 262252.2 on each sides, we get

Residual sum of squares = 310756.8-262252.2 = 48504.6

(3) Estimated coefficient of number of baths from the data table is 24.34. (it is given in the table)

(4) The percentage of variation in the price is accounted for by the regression equation is known as the R square value which is given equal to 0.844

converting it into percetage, we get 0.844*100 = 84.4%

so, 84.4 percentage of variation in the price is accounted for by the regression equation

option B is correct

(5) we know that the regression equation is

Price = 11.37 + 44.58*sqft + 24.34*bath +25.65*acreage

it is given that we have to use sqft = 2.5, number of baths = 3 and acreage = 1.25

setting the values in the above regression equation, we get

Price = 11.37 + 44.58*2.5 + 24.34*3 +25.65*1.25 = 11.37 + 111.45 + 73.02 + 32.0625 = 227.9025

so, this is equal to 227.9025*1000 = $227902.5

So, the required of price in equation is 227.9025 which is equal to $227902.5

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