Question 9-119 Pointsl According to the data obtained from a county egressions b

Question

Question 9-119 Pointsl According to the data obtained from a county egressions base on the a) 13 points] The market value of a house is typically related to its size. auditor regarding the age and current market value of houses in a particular subdivision, we ran i following mathematical functions: linear function, logarithmic function, and polynomial function (2nd order) as per below. The independent variable, X, is the number of square feet, and the dependent variable, Y, is the market value. Function y 63670ln(x)- 380884 y 0.0005x 33.137x 34401 y-35036x + 32673 R value 0.53048 0.53474 0.53473 Which mathematical function is the best fit, linear function, logarithmic function, or polynomial function (2nd order)? Why? Make predictions of market values for homes with 1600, 1679, and 1768 square feet respectively b) [6 points] According to data on sales dollars and the number of radio, TV, and newspaper ads promoting concerts for a group of cities, we developed a multiple linear regression model using both independent variables (Number of Radio & TV Ads (in thousands) and Number of Newspaper Ads (in thousands)). A part of the regression report is as per below Standard Coefficients Error 385.3814221 237.7349328 12.03232224 2.704912709 9.391870119 5.9826236 Intercept Radio&TV; ads Newspaper ads Make predictions of concert sales for the following situations: 1) 40,000 Radio & TV Ads and 40,000 Newspaper Ads; 2) 45,000 Radio & TV Ads and 50,000 Newspaper Ads.

Explanation / Answer

a).

R-squared is a statistical measure of how close the data are to the fitted regression line. It is also

R-squared = Explained variation / Total variation

R-squared is always between 0 and 100%:

R-squared is based on the underlying assumption that you are fitting a linear model. If you aren’t fitting a linear model, you shouldn’t use it. For Non-linear regression R-squared value is not reliable.

So we will take linear function for the best fit.

X

Y= 35.036 x + 32673

1600

88730.6

1679

91498.444

1768

94616.648

b).

Coefficients

Variable

Intercept

385.3814221

I

Radio&TV ads

12.03232224

R

Newspaper ads

9.391870119

N

Radio&TV ads

Newspaper ads

1

40000

40000

2

45000

50000

Regression Equation

Y= I + 12.03232224* R + 9.391870119 * N

Radio&TV ads(R)

Newspaper ads(N)

Y

1

40000

40000

857353.1

2

45000

50000

1011433

X

Y= 35.036 x + 32673

1600

88730.6

1679

91498.444

1768

94616.648

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