Question

Please type answer in word and include how you solved it and work in the word document.

The following table shows the overall GMAT scores of ten randomly selected participants and the number of hours they studied per week:

Score	Avg. weekly hours
550	12
380	18
430	21
600	20
650	48
680	21
540	14
750	56
710	40
400	10

a.       Identify the variables.

b.      Calculate and interpret the correlation coefficient.

c.       Perform a hypothesis test to determine if the population correlation coefficient (ρ) is significantly different from zero [α = 0.10].

d.      Estimate the regression equation (calculate bo and b1). Interpret the slope coefficient. Predict the score for a participant who, on an average, studies 20 hours per week.

e.       Calculate the coefficient of determination and interpret your results

Answer 1

Solution

a.       Identify the variables.

Dependent variable : Score Avg

Independent variable : weekly hours

for remaining questions we will find the solution using 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	0.7304
R Square	0.5334
Adjusted R Square	0.4751
Standard Error	95.7770
Observations	10.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	1.0000	83904.0843	83904.0843	9.1466	0.0165
Residual	8.0000	73385.9157	9173.2395
Total	9.0000	157290.0000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	412.8435	59.8608	6.8967	0.0001	274.8041	550.8829	211.9872	613.6998
weekly hours	6.0060	1.9859	3.0243	0.0165	1.4265	10.5855	-0.6574	12.6695

b.      Calculate and interpret the correlation coefficient.

correlation coefficient r = 0.7304

It can be interpreted as the relationship between Score Avg and Weekly Hours are positively correlated.

c. Perform a hypothesis test to determine if the population correlation coefficient (ρ) is significantly different from zero

The following needs to be tested: H :p=0 HA :p=0 where p corresponds to the population correlation. The sample size is n = 10, so then the number of degrees of freedom is df = n – 2 = 10 – 2 = 8 The corresponding t-statistic to test for the significance of the correlation is: n-2 t=r = 0.7304 10 – 2 1-0.73042 = 3.025 p2 The p-value is computed as follows: p= Pr( ts >3.025) = 0.0164 Since we have that p=0.0164 <0.10, it is concluded that the null hypothesis Ho is rejected. Therefore, based on the sample correlation provided, it is concluded that there is enough evidence to claim that the population correlation p is different than 0, at the 0.10 significance level.

d.      Estimate the regression equation (calculate bo and b1)

Score Avg = 412.8435+6.0060* weekly hours

Interpret the slope coefficient.

slope coefficient = 6.0060 , As we increase the weekly hours by 1 hours then average score will be increased by 6.0060.

Predict the score for a participant who, on an average, studies 20 hours per week.

Score Avg = 412.8435+6.0060*20

Score Avg = 532.9635

e.       Calculate the coefficient of determination and interpret your results

coefficient of determination = 0.5334

It explains 53.34% variation in Score Avg by weekly hours.