please assist with this NON GRADED problem Hint(s) Check MThe admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high-school GPA.ŷ = -1.41 + 0.0235a1 + 0.00486x2where¤1 = high-school grade point average22 = SAT mathemathics scorey = final college grade point averageRound test statistic values to 2 decimal places and all other values to 4 decimal places, Do not round vour intermediate calculations.a. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers.SUMMARY OUTPUTRegression StatisticsMultiple RR SquareAdjusted R SquareStandard ErrorObservationsANOVAdfMSSignificance FRegression1.76209ResidualTotal1.88CoefficientsStandard Errort StatP-valueIntercept-1.40530.4848X10.0234670.0086666X20.004860.001077

Answered: he admissions officer for Clearwater…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS

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please assist with this NON GRADED problem

Hint(s) Check M
The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student's SAT mathematics score and high-school GPA.
ŷ = -1.41 + 0.0235a1 + 0.00486x2
where
¤1 = high-school grade point average
22 = SAT mathemathics score
y = final college grade point average
Round test statistic values to 2 decimal places and all other values to 4 decimal places, Do not round vour intermediate calculations.
a. Complete the missing entries in this Excel Regression tool output. Enter negative values as negative numbers.
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
ANOVA
df
MS
Significance F
Regression
1.76209
Residual
Total
1.88
Coefficients
Standard Error
t Stat
P-value
Intercept
-1.4053
0.4848
X1
0.023467
0.0086666
X2
0.00486
0.001077

Expert Solution

Step 1

Given Information:

The admissions officer for Clearwater college developed the following estimated regression equations relating the final college GPA to the student's SAT mathematics score and high school GPA.

To complete the missing entries in the table:

First lets start with ANOVA:

Degrees of freedom of Regression is the number of independent variables. Since, there are two independent variables $x_{1}$ and $x_{2}$ .

$d f (R e g r e s s i o n) = 2$

$\begin{array}{rcl} d f (R e s i d u a l) & = & d f (T o t a l) - d f (R e g r e s s i o n) \\ = & 9 - 2 \\ = & 7 \end{array}$

Sum of Squares of Residuals is obtained as:

$\begin{array}{rcl} S S E & = & S S T - S S R \\ = & 1.88 - 1.76209 \\ = & 0.11791 \\ \approx & 0.1179 \end{array}$

Mean Sum of squares of Residual (Error) is given by the formula:

$\begin{array}{rcl} M S E & = & \frac{S S E}{d f (R e s i d u a l)} \\ = & \frac{0.1179}{7} \\ = & 0.01684285714 \\ \approx & 0.0168 \end{array}$

Mean Sum squares of Regression:

$\begin{array}{rcl} M S R & = & \frac{S S R}{d f (R e g r e s s i o n)} \\ = & \frac{1.76209}{2} \\ = & 0.881045 \end{array}$

F-statistic is given by the formula:

$\begin{array}{rcl} F & = & \frac{M S R}{M S E} \\ = & \frac{0.881045}{0.01684285714} \\ = & 52.31 \end{array}$

Using Excel function "=F.DIST.RT(52.31,2,7)", p-value obtained is 0.0001

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