Question

A basketball enthusiast collected data on the scoring statistics of the 2018-2019 Golden State Warriors. He wanted to know if he could use Field Goals Made (FGM) to predict Free Throws Made (FT). He ran a regression analysis and created the following regression equation and supplementary material. Assume that all the conditions are met. Parameter Std. Err. DF Intercept 0.28903828 15 Slope 0.065672563 15 Predicted Free Throws -0.3604 +0.4833(Field Goals) a) Interpret the slope of the regression equation For every additional free throw made, we predict the number of eldgoals made to increase, on average, by 0.4833 for every additional field goal made, we predict the number of free tom made to increason weg, by 0.4833 For every additional field pool made, we predict the number of the vows made to increase on erage, by -0.004 For every additional free throw made, we predict the number of field is made to increase, on avera, by 0.1004 b) That wason, Jonas Jerebko averaged 2.2 Meld goals and 0.9 free throws. What is the residual for Jonas Jerebko? (decimal places) Jonas Jerebke had a residual of indicating that he made fewer field goals than predicted he made more field goals than predicted he made for free throws than predicted he made more free throws than predicted

Answer 1

Q1 ( Image 1 )

Given

Parameter	Std. Err.	DF
Intercept	0.29803828	15
Slope	0.065672563	15

Regression equation is

Predicted Free Throws = -0.3604 + 0.4833 ( Feild goals )

Let   y - Free Throws      and        x - Feild goals

Then Regression equation is given by

= -0.3604 + 0.4833 * x

:

Estimate of intercept and slope are

Intercept a = -0.3604

Slope b = 0.4833

i)

Estimate of slope can be interpreted as , for every one unit increament in independent variable x , there will be increament of b=0.4833 in dependent variable y .

Hence correct option is

Option B.) For every additional feild goal made we predict number of free throw made to increase , on average , ny 0.4833

ii)

Jerebko averaged 2.2 feild goals and 0.9 free throws

hence x = 2.2         and          y = 0.9

So observed value is 0.9

Now predicted free throws are

= -0.3604 + 0.4833 * x

:

   = -0.3604 + 0.4833 * 2.2

= 0.70286

:

Residual is given by difference between observed value and predicted value of dependent variable (here free throws)

Residual = y -

:

              = 0.9 - 0.70286   =   0.19714

Residual = 0.19714

Since Here observed value y = 0.9 which is greater that predicted value = 0.70286 , we can say that he made more free throws than predicted

:

So correct option is

Jonas Jerebko has a residual of 0.19714 , indicating that

option D) indicating that he made more free throws than predicted

Q2 ( Image 2)

Average life span of women 1 = 80.7

r

Average life span of men 2 = 76.2

r

Given DF= 312.7 and standard error SE = 2.659

We want to test the difference in order women-men i.e
r
1-
r
2

Test statistics TS value is given by

TS = $\frac{\bar{x1}-\bar{x2}}{SE}$

     = $\frac{80.7-76.2}{2.659}$ = 1.692366 $\approx$ 1.692

TS = 1.692

So calculated test statistics value is 1.692