Question

1. Complete a full regression analysis of the student data below: Student Math Placement Calculus Sketch the Scatterplot Test Grade sketch and interpret the residual plot 1 39 65 write the regression equation 2 43 78 interpret the regression coefficient 21 52 interpret the correlation coefficient and 64 82 coefficient of determination. 5 57 92 6 47 89 7 28 73 8 75 98 What is the predicted grade of a student who scores a "60" on the placement test? 34 56 10 52 75

Answer 1

x = math placement test

y = calculus grade

У 120 100 80 60 0 10 30 40 50 60 70 80 20 40 20

Using Excel

data -> data analysis -> regression

x Residual Plot 15 10 10 30 70 80 -5 -10 -15 X 60 50 40 20 Ln O Residuals

residuals are randomly distributed

hence assumptions are satisfied

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8398
R Square	0.7052
Adjusted R Square	0.6684
Standard Error	8.7036
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1449.9741	1449.9741	19.1408	0.0024
Residual	8	606.0259	75.7532
Total	9	2056.0000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	40.7842	8.5069	4.7943	0.0014	21.1673	60.4010
x	0.7656	0.1750	4.3750	0.0024	0.3620	1.1691

y^ = 40.7842 + 0.7656* x

slope is 0.7656

it means when math placement test score increases by 1, calculus grade increases by 0.7656 on average

correlation coefficient = 0.8398

it means that there is strong and positive correlation between x and y

coefficient of determination = 0.7052

it means 70.52% of variance is explained by the model

y^ = 40.7842 + 0.7656* x

= 40.7842 + 0.7656* 60

= 86.7202

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