Question

1. This same researcher collected at random one child from each of the eight families in which there was at least one child. She recorded the following data to study the effects of number of siblings (X) on happiness of the child (Y), measured on an interval scale in which low scores indicate a low level of happiness and high scores indicate a high level of happiness:

                 X                  Y    

                 1                   5

                 0                   3

                 2                   4

                 4                   7

                 2                   5

                 3                   9

                 1                   8

                 1                   4    

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. See problem 1 for an explanation of the guidelines for interpretation.
3. Draw the regression line on the scatter plot.
4. Predict the happiness of an only child and the happiness of a child with two siblings.
5. Find the coefficients of determination and non-determination and interpret what they mean.
6. Is the relationship between education and number of children statistically significant using a 95% confidence level?

Answer 1

A)Scatterplot

B)The regression equation is y = 3.913 + .9783 x

For an unit increase in x , there is an increase of .9783 unit in y

When x = 0, y takes the value 3.913

C)

D)When number of siblings is 0, then the happiness of child is 3.913

When number of siblings is 2 , the happiness of child is 5.8696

E) Coefficient of determination is 0.3453 and so it explains 35% of variation in the model is explained by the independent variable

Coefficient of non determination is .6547 , and so 65% is the amount of unexplained variance

F)Since the p value is greater than the level of significance (.05) ,we accept the null hypothesis and conclude that there is no significant relationship between happiness and number of children