Question

Name the test or tests that are appropriate to answer the following questions.

(a) Whether the slope of the best fit line is different from zero?

(b) Whether the slope of the best fit line is greater than 1?

(c) Whether the intercept is different from zero?

(d) Whether the intercept is less than - 3?

These questions are related to Regression. Please explain why these tests would be best so I can understand.

Answer 1

SOLUTION A: TO TEST SLOPE whether it is equal to zero or not WE USE t test for testing slope with the formula

where b1 is slope we got from estimation

is true null hypothesis slope

and S.E is standard error of estimate of b1 coefficients

SOLUTION B: TO TEST SLOPE whether it is GREATER THAN 1  WE USE t test for testing slope with the formula

where b1 is slope we got from estimation

is true null hypothesis slope . and equal to 1 in this case.

and S.E is standard error of estimate of b1 coefficients

SOLUTION C: TO TEST intercept whether it is different from zero WE USE t test for testing intercept with the formula

where b0 is intercept we got from estimation

is true null hypothesis slope and equal to 0 in this case.

and S.E is standard error of estimate of b0 coefficients

SOLUTION D: TO TEST INTERCEPT whether it is SMALLER THAN -3 WE USE t test for testing intercept with the formula

where b0 is INTERCEPT we got from estimation

is true null hypothesis INTERCEPT VALUE . and equal to -3 in this case.

and S.E is standard error of estimate of b0 coefficients

I hope this will help you.