Question

1. A family researcher is interested whether there is an association between the number of siblings a person has and the number of children they have. She interviews six older adults and finds the following information.

Number of Siblings	Number of Children
0	1
1	1
2	1
2	0
3	3
4	3
Mean Number of Siblings = 2	Mean Number of Children = 1.5
Standard Deviation = 2	Standard Deviation = 1.5

1. Explain which variable more naturally plays the role of the independent variable, and which the dependent. (2 points)

2. Calculate the correlation coefficient. (8 points)

x	y

3. Write a sentence to interpret the correlation coefficient. (2 points)

4. Conduct a hypothesis test to see whether the association between number of siblings and number of children is statistically significant or not at the level of α = .01. Write a sentence to interpret your answer. (4 points)

5. Calculate and interpret the meaning of the regression slope. (4 points)

6. Calculate and interpret the meaning of the Y-intercept for the regression line. (4 points)

7. Would you feel comfortable predicting the value of Y when X = 6? If so, make the prediction. If not, explain why not. (2 points)

Answer 1

a) independent = number of sibling

dependent= number of children

b)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	12.00	9.00	10.00	7.50	6.00
mean	2.00	1.50	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.6928

c) there is moderate positive linear relationship

d)

Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   6  
alpha,α =    0.01  
correlation , r=   0.6928  
t-test statistic = r*√(n-2)/√(1-r²) =        1.922
DF=n-2 =   4  
p-value =    0.1270  
Decison:   P value > α, So, Do not reject Ho  

e)

estimated slope , ß1 = SSxy/SSxx =   6.0   /   10.000   =   0.6000
                  
f) intercept,   ß0 = y̅-ß1* x̄ =   0.30000          

g) No,  you would not feel comfortable predicting the value of Y when X = 6

because regression model is not significant