Mathematics: A regression analysis was done of residential property values in a portion of a city. The dependent variable is Sale Price (Y) and the independent variable is Square Footage (X). Data for 157 properties were used in the regression. The results are listed below. Predicted Y = 96,600 + 22.5(X) R-square = .77 What is the predicted value of Sale Price if the property has 2500 square feet? A. $56,250.00 B. $152,850.00 C. $96,622.50 D. $96,600.00

H=2 i just took the testStep-by-step explanation:...

A regression analysis was done of residential property

emma5743

18.01.2022

Y= 96600+ 22.5*2500= 152850

So then the correct option for this case would be:

B. $152,850.00

Step-by-step explanation:

They adjust a linear model y = mx +b using the least squares method

For this case we assume that they calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

$\bar X =\frac{\sum X}{n}$

$\bar Y =\frac{\sum Y}{n}$

And we can find the intercept using this:

$b=\bar y -m \bar x$

After apply the method they obtain the following regression equation:

Y = 96600 + 22.5 X

Where Y represent the sale price and X the square footage.

And we want to estimate the predicted value of Sale price if the property has a 2500 square footage.

So for this case we just need to replace into our original equation the value of X = 2500 and we got:

Y= 96600+ 22.5*2500= 152850

So then the correct option for this case would be:

B. $152,850.00

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