Question

Use the following regression data for parts A-D: In-state and out-of-state tuition was recorded for a sample of public colleges in the U.S., and a regression was performed which gave the following output:

The regression equation is:   Out-of-State = 4226 + 1.79 In-State

Predictor        Coef     SE Coef          T        P

Constant         4226        3686       1.15    0.281

In-State       1.7903      0.5256       3.41    0.008

S = 3034        R-Sq = 56.3%     R-Sq(adj) = 51.5%

A) What is the response variable for this regression?

a) in-state tuition

b) out-of-state tuition

B) From the output, determine the value of r, the correlation coefficient:

a)   3034

b) 56.3%

c) 75%

C) Use the line of regression to predict the cost of out-of-state tuition for a college that charges $15,000 for in-state tuition.

            a) $31,076

            b) $19,226

            c) $4,226

D) Interpret the slope of this regression line, in context:

            a) When in-state tuition is $0, out-of-state tuition is predicted to be $4,226.

            b) When out-of-state tuition is $0, in-state tuition is predicted to be $4,226.

c) For every increase of $1 in out-of-state tuition, in-state tuition is predicted to go up by $1.79.

d) For every increase of $1 of in-state tuition, out-of-state tuition is predicted to go up by $1.79.

Answer 1

Given :

The regression equation is:   

Out-of-State = 4226 + 1.79 In-State

A) The outcome variable in regression equation is called Response vatiable or dependent variable.

In equation y = a+bx , y is the response vatiable.

So Out-of-State is the response vatiable.

Therefore the option choice b) out-of-state tuition is the answer.

B) In the regression output we have given the R-Sq =56.3%

That is r​​​​​​2 ​​​​​​= 0.563

Taking square root we get ,

r = 0.750

That is r = 75%

Therefore the correlation coefficient is 75%

Answer choice c) 75% is the answer.

C) Given : in-state tuition = $15,000

Out-of-State = 4226 + 1.79 In-State

= 4226 + 1.79*15000

= 31076

Out-of-State = $31,076

So the cost of out-of-state tuition for a college that charges $15,000 for in-state tuition is $31,076

Therefore the choice a) $31,076 is correct.

D)

In regression line y = a+bx , b is the slope.

Out-of-State = 4226 + 1.79 In-State

Therefore the slope is 1.79

As slope is positive,as x increases y is also increase.

So for every increase of $1 of in-state tuition, out-of-state tuition is predicted to go up by $1.79

Therefore for choice d) is the answer.