Question

1a) Here is a bivariate data set.

x	y
26.1	41.5
26.6	46.9
37.2	44.2
37.2	46.6
34.1	44.1
33.8	38.4
39.9	30
12.4	66.8
8.1	49.6
13.4	61.6
15	52.4
21.8	61.6
3.6	53.9
-9.3	97.2
28.3	39.4
29.4	44.9
29.8	41.2

Find the correlation coefficient and report it accurate to three decimal places.
r =

What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.
r² = %

part b)You wish to determine if there is a negative linear correlation between the two variables at a significance level of α=0.005α=0.005. You have the following bivariate data set.

x	y
23.3	60.3
17	54.3
-2.7	68.7
14.7	59.5
49.6	41.7
10.5	57.7
21.8	48.5
14.9	56.7
37.2	46.4
29.2	42.5
30.4	50.7
10.2	58.1

What is the correlation coefficient for this data set?
r =

To find the p-value for a correlation coefficient, you need to convert to a t-score:

t=√r2(n−2)1−r2t=r2(n-2)1-r2

This t-score is from a t-distribution with n–2 degrees of freedom.

What is the p-value for this correlation coefficient?
p-value =

Your final conclusion is that...

• There is insufficient sample evidence to support the claim the there is a negative correlation between the two variables.
• There is sufficient sample evidence to support the claim that there is a statistically significant negative correlation between the two variables.

can you please show the work on a ti 84 plus as well please thank you so much

Answer 1

1)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	387.4	860.3	2977.457647	3706.3	-2760.22
mean	22.79	50.61	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.8309

.........

R² =    (Sxy)²/(Sx.Sy) =    0.6904
69% of the variation in y can be explained by the variation in the values of x

........

correlation hypothesis test      
Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   17  
alpha,α =    0.005  
correlation , r=   -0.8309  
t-test statistic = r*√(n-2)/√(1-r²) =        -5.783
DF=n-2 =   15  
p-value =    0.0000  
Decison:   p value < α , So, Reject Ho

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

2)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	256.1	645.1	2122.009167	705.6	-1072.98
mean	21.34	53.76	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.8768
correlation hypothesis test      
Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   12  
alpha,α =    0.005  
correlation , r=   -0.8768  
t-test statistic = r*√(n-2)/√(1-r²) =        -5.767
DF=n-2 =   10  
p-value =    0.0002  
Decison:   p value < α , So, Reject Ho  

There is sufficient sample evidence to support the claim that there is a statistically significant negative correlation between the two variables.

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

THANKS

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