Question

bus A study was done to look at the relationship between number of lovers college students have had in their lifetimes and their GPAs. The results of the survey are shown below. ules es Lovers GPA 2 4 4 6 2.63.22.8 2.6 3.23.1 2.9 2.4 2.3 ale e 365 edia ia Gallery ary les Tuition ment edible a. Find the correlation coefficient: Round to 2 decimal places. b. The null and alternative hypotheses for correlation are: HO:?V0 H:? The p-value is: (Round to four decimal places) c. Use a level of significance of a -0.06 to state the conclusion of the hypothesis test in the context of the study. o There is statistically significant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. o There is statistically insignificant evidence to conclude that a student who has had more lovers will have a lower GPA than a student who has had fewer lovers. There is statistically significant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is useful There is statistically insignificant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the use of the regression line is not appropriate d. (Round to two decimal places) e. Interpret-2: Given any group of students who have all had the same number of lovers, 53% of all of these studetns will have the predicted GPA. o There is a 53% chance that the regression line will be a good predictor for GPA based on the number of lovers a student has had. 0 53% of all students will have the average GPA. o There is a large variation in students GPAs, but if you only look at students who have had a fixed number of lovers, this variation on average is reduced by 53%. 1. The equation of the linear regression line is: (Please show your answers to two decimal places) g. Use the model to predict the GPA of a college student who as had lovers. GPA- (Please round your answer to one decimal place.) h. Interpret the slope of the regression line in the context of the question: For every additional lover students have their GPA tends to decrease by 0.12. The slope has no practical meaning since a GPA cannot be negative. As x goes up, y goes down. 1. Interpret the y-intercept in the context of the question: The best prediction for the GPA of a student who has never had a lover is 3.23. olf a student has never had a lover, then that student's GPA will be 3.23. The y-intercept has no practical meaning for this study, The average GPA for all students is predicted to be 3.23.

Answer 1

a)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	34.00	25.10	35.56	0.91	-4.12
mean	3.78	2.79	SSxx	SSyy	SSxy

correlation coefficient ,    r = SSxy/√(SSx.SSy) =   -0.725

..............

b)

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   9  
alpha,α =    0.05  
correlation , r=   -0.7251  
t-test statistic = r*√(n-2)/√(1-r²) =        -2.7861
DF=n-2 =   7  
p-value =    0.0271  
Decison:   p value < α , So, Reject Ho  
.

c)

There is statistically significant evidence to conclude that there is a correlation between the number of lovers students have had in their lifetimes and their GPA. Thus, the regression line is useful.

.................

d)

R² =    (SSxy)²/(SSx.SSy) =    0.53

e)

There is a 53% chance that the regression line will be a good predictor for GPA based on the number of lovers a student has had.

.........

f)

Sample size,   n =   9      
here, x̅ = Σx / n=   3.778          
ȳ = Σy/n =   2.789          
SSxx =    Σ(x-x̅)² =    35.5556      
SSxy=   Σ(x-x̅)(y-ȳ) =   -4.1      
              
estimated slope , ß1 = SSxy/SSxx =   -4.1222/35.5556=   -0.1159      
intercept,ß0 = y̅-ß1* x̄ =   2.7889- (-0.1159 )*3.7778=   3.2269      
              
Regression line is, Ŷ=   3.23   + (   -0.12   )*x

....

g)

Predicted Y at X=   5   is          
Ŷ=   3.22688   +   -0.11594   *5=   2.6

.....

h)

.

O For every additional lover students have, their GPA tends to decrease by 0.12.

i)

The best prediction for the GPA of a student who has never had a lover is 3.23.

............

Please let me know in case of any doubt.

Thanks in advance!

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