Given below are seven observations collected in a regression

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel\'s Regression Tool to answer the following questions. x y 2 12 3 9 6 8 7 7 8 6 7 5 9 2 a. What is the estimated regression equation? b. Perform a t test and determine whether or not x and y are related. Use = 0.05. c. Perform an F test and determine whether or not x and y are related. Use = 0.05. d. Find and interpret the coefficient of determination. step by step with formula than you

Solution

The regression equation is
y = 13.8 - 1.12 x

Predictor Coef SE Coef T P
Constant 13.750 1.398 9.83 0.000
x -1.1250 0.2165 -5.20 0.003

S = 1.36931 R-Sq = 84.4% R-Sq(adj) = 81.3%

Answer of the excel output,

Analysis of Variance

Source DF SS MS F P
Regression 1 50.625 50.625 27.00 0.003
Residual Error 5 9.375 1.875
Total 6 60.000

a. What is the estimated regression equation?

y = 13.8 - 1.12 x

b. Perform a t test and determine whether or not x and y are related. Use = 0.05.

Predictor Coef SE Coef T P
Constant 13.750 1.398 9.83 0.000
x -1.1250 0.2165 -5.20 0.003

as the p-value corresponding to x is 0.003<0.05 so are rejecting H0 and claim that there is a relation in x and y

c. Perform an F test and determine whether or not x and y are related. Use = 0.05.

Source DF SS MS F P
Regression 1 50.625 50.625 27.00 0.003
Residual Error 5 9.375 1.875
Total 6 60.000

here also the corresponding to the regression coefficient p-value=0.003<0.05. hence we are rejecting H0 and claim that there is a relation in x and y

. d) Find and interpret the coefficient of determination.

coefficient of determination R-Sq = 84.4%

there is modarate high relation in x and y showing

here R²=1-(residual error / total ss)=1-(9.375/60)=0.844