Question

Suppose we have a simple linear regression with following printout.

Coefficients:

                        Estimate Std.    Error    t value Pr(>|t|)

(Intercept)        -0.06811     0.08375      -0.813      0.421

X                     0.86818     0.40886      2.1234      0.046

a. What is the p-value for testing the slope H₀: β₁=0 vs. H_a: β₁>0?

b. Suppose we had a. F-test for adequacy of this regression. What is the value of the test statistic?

What is the p-value?

c. Suppose the sample correlation coefficient of x and y is 0. 852.How much of the variation of y can be

Explained by this regression?

Answer 1

Answer: Suppose we have a simple linear regression with following printout.

Solution:

a) The p-value for testing the slope H0: β1=0 vs. Ha: β1>0:

p-value = 0.046

b) Suppose we had a. F-test for adequacy of this regression, the value of the test statistic:

test statistic = 2.1234

the p-value = 0.046

c. Suppose the sample correlation coefficient of x and y is 0. 852.

r = Corr(x,y) = 0.852

Therefore,

r​​​​​​2​​​​​ = (0.852)2  = 0.7259

The variation of y can be explained by this regression:

72.59% of the variation of y can be explained by this regression.