Question

Use the following data set to calculate the regression equation. What would you estimate the happiness rating for someone who has 5 children to be?

Number of children	Happiness Rating
2	1
5	5
8	6
4	3
5	5
6	7
1	2
6	5
3	2

Answer 1

Based on the given data, our objective is to  estimate the happiness rating for someone who has 5 children. The dependent variable here, would be the happiness rating and the independent variable would be Number of children. Regressing Happiness rating on Number of children, we get the fitted regression of the form:

where = Estimated Happiness rating, x = No. of Children, a = Estimated Intercept Coefficient and    b = Estimated Slope coefficient

The estimated regression coefficients can be obtained using the formula:

and

Substituting the values,

= 0.8372

Hence,

  

= 0.2791

Hence, the fitted regression equation is given by:

In order to estimate the happiness rating for someone who has 5 children, we may substitute x = 5 in the above expression:

= 4.4651

Hence, the happiness rating for someone who has 5 children is estimated to be 4.