Question

A researcher collected the following data on years of education (X) and number of children (Y) for a sample of married adults:

X	Y
12	2
14	1
17	0
10	3
8	5
9	3
12	4
14	2
18	0
16	2

a. Draw a scatterplot of the data.

b. Calculate the correlation between education and number of children for this sample of 10 married adults.

c. Interpret the correlation between education and number of children.

d. Is the association between education and number of children statistically significant at the alpha level of .005? Provide a full interpretation of your answer.

e. Calculate and interpret the meaning of the regression slope.

f. Calculate and interpret the meaning of the Y-intercept for the regression line.

g. Predict the number of children for an adult with 11 years of education.

h. Predict the number of children for an adult with 1100 years of education. What two limitations of prediction from a regression line does this example demonstrate?

Answer 1

a)

b)

c) linear decreasing trend

d)

Degree of freedom (df) can be found out by n-2, where n is number of data points

df = n-2

df = 10-2

df = 8

\alpha = 0.05

critical value @ (df = 8 and \alpha = 0.05) = 0.632Since, r = -0.868 is less than -0.632. Therefore, r is significant

decrease of no of children by increase in year of education by factor of 0.4135

maximum 7 child at max when o education

this graph will work till 18 as the minimum possible value will be zero

at year of education can't be more than 40(in practical)