Use the following set of data points to complete the problems listed below. Cons
ID: 3170073 • Letter: U
Question
Use the following set of data points to complete the problems listed below. Construct the linear regression equation for the set of data points. Specify the values for b_1 and b_0 b_1 =___ b_0 = ___ Predict the expected y value for x = 25. y =___ Calculate the correlation coefficient (Pearson's r) for the set of data points. r =___ From the choices below, choose the best description of the correlation found in problem 3 and briefly explain in words the reason/rationale for your selection. a). Strong positive correlation___ b). Moderate positive correlation___ c). Virtually no correlation___Explanation / Answer
from above
1)hence b1=Sxy/Sxx=(-133.5)/157.88=-0.846
and bo=Ybar-b1*Xbar=82.5-(-0.846)*14.63 =94.867
2)for x=25; y=-0.846*25+94.867 =73.727
3)r=(Sxy/(Sxx*Syy)1/2=-0.775
4) there exist a moderate negative correlation as value of r is considerable and negative,
x y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi' (Y-Yi')^2 10.00 92.00 21.39 90.25 -688.75 86.41093 31.2377441 15.00 81.00 0.14 2.25 101.25 82.1829 1.39924735 12.00 84.00 6.89 2.25 -105.75 84.71971 0.51798963 20.00 74.00 28.89 72.25 531.25 77.95487 15.6409916 8.00 85.00 43.89 6.25 -186.25 88.10214 9.62325873 16.00 80.00 1.89 6.25 166.25 81.33729 1.78835033 14.00 84.00 0.39 2.25 -102.75 83.0285 0.94380533 22.00 80.00 54.39 6.25 151.25 76.26366 13.9602519 Total 117.00 660.00 157.88 188.00 -133.50 75.111639 mean 14.63 82.50 Sxx Syy Sxy