Question

The data below shows data collected at the end of a statistics class to investigate the relationship between x = study time per week (average number of hours) and y = college GPA. The table shows the data for the 8 males in the class on these variables and on the number of class lectures of the course that the student reported skipping during the term.

Is there a statistically significant correlation between study time and GPA at the .05 significance level? If yes what is the p-value?

If there is a statistically significant correlation what would the formula be to predict GPA based on study time?

If there is a statistically significant correlation what would the GPA be estimated for studying 0 hours?

If there is a statistically significant correlation what would the GPA be estimated for studying 9 hours?

Student	Study time	GPA	Skipped
1	14	2.8	9
2	25	3.6	0
3	15	3.4	2
4	5	3	5
5	10	3.1	3
6	12	3.3	2
7	5	2.7	12
8	21	3.8	1

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
14	2.8	0.3906	0.1702	-0.2578
25	3.6	135.1406	0.1502	4.5047
15	3.4	2.6406	0.0352	0.3047
5	3	70.1406	0.0452	1.7797
10	3.1	11.3906	0.0127	0.3797
12	3.3	1.8906	0.0077	-0.1203
5	2.7	70.1406	0.2627	4.2922
21	3.8	58.1406	0.3452	4.4797

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	107.00	25.70	349.88	1.03	15.36
mean	13.38	3.21	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.8097

yes, there a statistically significant correlation between study time and GPA at the .05 significance lev

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   8  
alpha,α =    0.05  
correlation , r=   0.8097  
t-test statistic = r*√(n-2)/√(1-r²) =        3.380
DF=n-2 =   6  
p-value =    0.0149  

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Ŷ =   2.625   +   0.044   *x
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Predicted Y at X=   0   is          
Ŷ =   2.6252   +   0.0439   *0=   2.625
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Predicted Y at X=   9   is          
Ŷ =   2.6252   +   0.0439   *9=   3.020