14. Run a regression analysis on the following bivariate set of data with y as t

Question

14. Run a regression analysis on the following bivariate set of data with y as the response variable.

Verify that the correlation is significant at an =0.05=0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 66.4 on the response variable.

What is the predicted explanatory value?
x =

(Report answer accurate to one decimal place.)

15.You run a regression analysis on a bivariate set of data (n=91n=91). With ¯x=26.7x¯=26.7 and ¯y=56.8y¯=56.8, you obtain the regression equation

y=0.398x+7.301y=-0.398x+7.301

with a correlation coefficient of r=0.959r=-0.959. You want to predict what value (on average) for the response variable will be obtained from a value of 60 as the explanatory variable.

What is the predicted response value?
y =

(Report answer accurate to one decimal place.)

x y 64.9 61.4 70.9 64 105.4 71.1 65.6 57 96.2 64.7 90.9 64.4 72.8 63.4 90.5 64.4 93.3 71.4 47.7 59.9 76.3 61.5 66.9 64.1 84.2 65.5 82.8 66.3

Explanation / Answer

14)

from above correlation coefficient r=(Sxy/(SSx*SSy)1/2 =0.7725

for test stat t=r*((n-2)/(1-r2))1/2 =14.599

for which p value=0

as p vlaue is less then 0.05; regression is significant

from above b1=Sxy/Sxx=0.1914

and Bo=Ybar-b1*Xbar=49.067

hence predicted value of independent variable at Y=66.4

X=(Y-bo)/b1=90.553

15) from above predicted response variable =-0.398*60+7.301 =-16.579

x y (X-Xbar)^2 (Y-Ybar)^2 (X-Xbar)(Y-Ybar) Yi' (Y-Yi')^2 64.90 61.40 203.67 7.96 -1.91 61.48981 0.0080665 70.90 64.00 68.42 0.05 -1.48 62.63824 1.85438926 105.40 71.10 687.94 47.31 283.25 69.24169 3.45330224 65.60 57.00 184.18 52.15 -9.96 61.6238 21.3794971 96.20 64.70 289.97 0.23 15.30 67.48077 7.73269752 90.90 64.40 137.56 0.03 4.76 66.46633 4.26971666 72.80 63.40 40.60 0.67 -7.05 63.00191 0.15847658 90.50 64.40 128.34 0.03 4.69 66.38977 3.95917468 93.30 71.40 199.62 51.53 208.74 66.9257 20.019361 47.70 59.90 990.45 18.67 71.40 58.19766 2.89797079 76.30 61.50 8.25 7.41 -32.87 63.67182 4.71682114 66.90 64.10 150.59 0.01 -0.33 61.87262 4.96121008 84.20 65.50 25.29 1.63 25.54 65.18392 0.09990689 82.80 66.30 13.17 4.32 38.62 64.91595 1.91558535 Total 1108.40 899.10 3128.03 192.02 598.72 77.4261758 mean 79.17 64.22 SSX Ssy Sxy

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