A real estate company wants to study the relationship between house sales prices

Question

A real estate company wants to study the relationship between house sales prices and some important predictors of sales prices. Based on data from recently sold homes in the area, the variables sales price (in thousands of dollars) x1total floor area (in square feet) x,-number of bedrooms x,-distance to nearest high school (in miles) are used in a multiple regression model. The estimated model is y-163 + 0.05 1x1 + Tz2-8r3. Answer the folowing questions for the interpretation of the coefficient of x1 in this model Holding the other variables fixed, what is the average change in sales price for each 100- square-foot increase in floor space? dollars increase decrease Is this change an increase or a decrease?

Explanation / Answer

Answer

we have the regression equation y = 163 + 0.051x1 + 17x2 -8x3

Now, we have to hold the variable x2 and x3 and put the value of x1 = 100 in the given equation

we get

y = 163 + 0.051*100 + constant .....................here 163, x2 and x3 terms are constants

so, the net change in y for x1 = 100

we get

y = 163 + 5.1 + constant

so, the value of y is $5.1 (increase)

So, first fill in the blank is $5.1

and second fill in the blank is increase

It is increase because the sign of x1 is positive, if the sign in front of x1 is negative, then we can say that the y is decreasing due to x1

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