Question

In: Statistics and Probability

The table below shows a measure of the “liberalness” of various American cities and a measure...

The table below shows a measure of the “liberalness” of various American cities and a measure of the corresponding asking price per square foot for housing.

Liberalness 1 0 6 7 10 15 16 19 22 25 26 30
Price 2 3 2 2 0 7 6 8 7 8 4 16

Enter the slope and y-intercept of the regression line, using liberalness as the independent variable. Round your answers to two decimal places.

Slope:         Intercept:

Enter the correlation coefficient and the coefficient of determination for the data. Round your answers to two decimal places.

Correlation coefficient:      Coefficient of determination:

Solutions

Expert Solution

x y (x-xbar)^2 (y-ybar)^2 (x-xbar)*(y-ybar)
1 2 189.0625 11.673611 46.97916667
0 3 217.5625 5.8402778 35.64583333
6 2 76.5625 11.673611 29.89583333
7 2 60.0625 11.673611 26.47916667
10 0 22.5625 29.340278 25.72916667
15 7 0.0625 2.5069444 0.395833333
16 6 1.5625 0.3402778 0.729166667
19 8 18.0625 6.6736111 10.97916667
22 7 52.5625 2.5069444 11.47916667
25 8 105.0625 6.6736111 26.47916667
26 4 126.5625 2.0069444 -15.9375
30 16 232.5625 112.00694 161.3958333
sum 177 65 1102.25 202.91667 360.25
mean 14.75 5.416666667 sxx syy sxy
slope=b1=sxy/sxx 0.326831481
intercept=b0=ybar-(slope*xbar) 0.595902321
SST SYY 202.91667
SSR sxy^2/sxx 117.74104
SSE syy-sxy^2/sxx 85.175626

slope (b1) = 0.33
intercept (bo) = 0.60

#Correlation=r=Sxy/sqrt(Sxx*Syy)

=360.25/sqrt(1102.25*202.91667)

r=0.7617

#Correlation coefficient=0.76

#Coefficent of determination=r^2

r^2=SSR/SST

=117.741/202.916

r^2=0.5802

#Coefficient of determination:=0.58


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