Question

The data below are scores of 8 randomly selected statistic students, and the number of hours they studied for their quiz.

x (hours)	3	2	4	6	3	2	4	8
y (scores)	65	60	85	90	71	57	83	96

a. Calculate the linear correlation coefficient and coefficient of determination and explain its meaning.   

b. Find the equation of the regression line and use it to predict the quiz score of a student who studied 5 hours.

c. Find the residual for the 7^th pair.   

e

BONUS: Draw a scatter plot diagram and graph the line of regression on the same plane.

Answer 1

Excel

we will solve it by using excel and the steps are

Enter the Data into excel

Click on Data tab

Click on Data Analysis

Select Regression

Select input Y Range as Range of dependent variable.

Select Input X Range as Range of independent variable

click on labels if your selecting data with labels

click on ok.

So this is the output of Regression in Excel.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9179
R Square	0.8426
Adjusted R Square	0.8164
Standard Error	6.2496
Observations	8.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	1.0000	1254.5333	1254.5333	32.1206	0.0013
Residual	6.0000	234.3417	39.0569
Total	7.0000	1488.8750
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	50.0083	5.0707	9.8621	0.0001	37.6007	62.4160
x (hours)	6.4667	1.1410	5.6675	0.0013	3.6747	9.2586

a. Calculate the linear correlation coefficient and coefficient of determination and explain its meaning.

linear correlation coefficient = 0.9179 which indicates that there is strong positive correlation between hours and scores.

coefficient of determination = 0.8426 which is interpreted as 84.25% variation in the model explained by hours.

b. Find the equation of the regression line and use it to predict the quiz score of a student who studied 5 hours

Scores = 50.0083+6.4667*hours

to predict the quiz score of a student who studied 5 hours.

Scores = 50.0083+6.4667*hours

Scores = 50.0083+6.4667*5

Scores = 82.3418

c. Find the residual for the 7th pair.

Observation	Predicted y (scores)	Residuals
7.0000	75.8750	7.1250

e

BONUS: Draw a scatter plot diagram and graph the line of regression on the same plane.