In: Statistics and Probability
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:
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