15. which of the following statements is true? a. if the calculated value of f statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis. b. the f statistic is always nonnegative as ssrr is never smaller than ssrur. c. degrees of freedom of a restricted model is always less than the degrees of freedom of an unrestricted model. d. the f statistic is more flexible than the t statistic to test a hypothesis with a single restriction

c) is true

Step-by-step explanation:

Given are four statements. Let us check one by one

a) If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis

False, we reject H0 in favour or alternate

b) The F statistic is always nonnegative as SSRr is never smaller than SSRur.

F statistics is non negative but reason is bot SSRr and SSRur are positive

Not because SSRr is never smaller than SSRur

c) Degrees of freedom of a restricted model is always less than the degrees of freedom of an unrestricted model.

This is true because in a restricted we put constraints thus df will be less

d) The F statistic is more flexible than the t statistic to test a hypothesis with a single restriction.

False.  F statistic is for testing variances while t statistic for means.

linear pair postulates

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)