Question

(Typed work preferable. Show step-by-step please.)

1. Suppose that a researcher collected the following set of data on years of education (X) and number of children 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. Write out the regression equation, then calculate and interpret the meaning of the regression slope and Y-intercept. You must provide both numbers and careful description of what both “a” and “b” mean. For the value of “a” (the Y-intercept), it is not sufficient to say it is the baseline. Your interpretation of both “a” and “b” should include reference to the specific units or metric of both variables. This is true for all questions asking you to interpret the slope and Y-intercept.

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

c. Report the coefficients of determination and non-determination and interpret what each of these statistics means.

d. Is the relationship between education and number of children statistically significant using a 99% confidence level?

Answer 1

Solution:-) Here, we want to analysis the data based on the married adults will have how many children as based on their years of education. So, the regression line will be Y=a+bx, where b is the slope that is how much X effect the Y, and a is interecept this means that if anyone who have not studied at all or years of education is zero, then how many children he will have.

All the caculations are done in R. On R.H.S. is code and on L.H.S. is output.

b) From above we have the regression line as

c) With 11 years of education we have

d) The coefficient of determination that is R squared is 75.33%. So, 75 % of the variability is explained by the model.

We can see that the p-value of intercept is <0.05. So, it significantly effect the model. This means that is any person who had not go to school once that is 0 years of education will have approx 8 children. Therefore education will lower the fertility rate.

e) The model is statistically significant or not will be seen the p-value of F statistic as p-value is 0.001131 < 0.01. Therefore the relation is statistically significant at 99 % confidence.