Question
A regression analysis of 117 homes for sale produced the following model, where price is in thousands of dollars and size is in square feet Price =47.88+0.068(Size) a) Explain what the slope of the line says about housing prices and house size b) What price would you predict for a 3500-square-foot house in this market? c) A real estate agent shows a potential buyer a 1200-square-foot house, saying that the asking price is $5500 less than what one would expect to pay for a house of this size. What is the asking price, and what is the $5500 called? a) Explain what the slope of the line says about housing prices and house size A. For every $1000 increase in price of a house, the size is predicted to increase by 0.068 square feet. OB. For every additional square foot of area of a house, the price is predicted to increase by $68. OC. For every $1 increase in price of a house, the size is predicted to increase by 68 square feet OD. For every additional square foot of area of a house, the price is predicted to increase by $0.068. b) What price would you predict for a 3500-square-foot house in this market? $0 c) A real estate agent shows a potential buyer a 1200-square-foot house, saying that the asking price is $5500 less than what one would expect to pay for a house of this size. What is the asking price? What is the $5500 called? QA. Predicted value OB. Intercept OC. Residual OD. Slope me
Answer
| s (a) : Option (b) is correct chioce For every additional square foot of area of a house , the price is predicted to be increased by $68 |
Support :
As we know that estimated regresion is represented as
Y(reponse variable) = intercept + Slope* predictor variables
.: E(y) = bo + b1* x
From developed regression output as highlighted below , we know that intercept = 47.86 and slope coefficient for predictor variable is 0.068
Independent variable are given as sqft size of home denoted by x
Dependent variable is given as sales price of home denoted by Y
Thus, regression equation is
Estimated y = 47.86 + 0.068*x
Regression model can also be defined in form of variable name as below:
Predicted Average price (in ‘000’s )= 47.86 + 0.068*Sqft
Interpretation of parameters :
Slope , b1 = This refers the change in response variable value when we increase unit change in explanatory variable..
In simple words, we can say that b1, slope is units by which response variable will change when we change one unit in explanatory variable.
In given case, and b1 = 0.068 . It means average home sales price will increase by $ 0.068 times with single unit increase in sqft . Since home sale price is 1000’s units, we willl multiply the 0.068 by 1000, we get value as $ 68
While option (a) is not correct choice because slope in regression measure changes in response variable , sales price in this case
option (c) is not correct choice because slope in regression measure chnages in response variable , sales price in this case
option (d) is not correct choice because chnage is $ 68 in response variable , since sales prices value are given in ‘000 units.
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