Question

1. Suppose that a researcher collected the following set of 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    

1. Draw a scatter plot of the data.
2. 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.
3. Draw the regression line on the scatter plot.
4. Predict the number of children for an adult with 11 years of education.
5. Report the coefficients of determination and non-determination and interpret what each of these statistics means.
6. Is the relationship between education and number of children statistically significant using a 99% confidence level?

Answer 1

(a) Scatter Diagram:

(b) Regression Equation of Y on X

	X	Y
	12	2
	14	1
	17	0
	10	3
	8	5
	9	3
	12	4
	14	2
	18	0
	16	2
MEAN	13.0000	2.2000
S.D	3.2249	1.5362
r	-0.8680

Here the Slope term b = -0.4135 and the Intercept term a = 7.5752

Therefore for every unit change in X there will the Constant Change in Y i.e -0.4135 (Slope Term). Intercept term is a constant term that will be just added to to product of slopeterm and X values.

X	Y = (-0.4135)X + 7.5752
12	2.6132
14	1.7862
17	0.5457
10	3.4402
8	4.2672
9	3.8537
12	2.6132
14	1.7862
18	0.1322

(c) Regression LIne on the Scatter Plot

I have posted the two figures above. The Second figure will clearly show the Concept. If you observe in the Second Diagram The Regression Line of Y on X formed a Straight Line from Top Left Corner to Bottom Right Corner.

(d) Given X = 11

Substitute X = 11 in the Regression Equation of Y on X

Therefore No: of Children(Y) = 3 at X = 11