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 happiness level and number of siblings statistically significant using a 95% confidence level?

Answer 1

( a )

(b )

So from the above output

Regression equation is

y = 3.9130 + 0.9783 x

Interpretation :

The slope indicates that every​ 1 person increase in number of siblings increases happiness of a child by 0.9783 on average

The​ y-intercept means that happiness of a child 3.9130 on average.

( c )

( d )

Given x = 2 then

y = 3.913 + 0.978 ( 2 )

y = 5.869

( e )

coefficients of determination ( r2 ) = 0.3453 ~ 34.53 %

coefficients of non-determination ( 1 - r2 ) = 0.6547 ~ 65.47%

34.53 % of variation in happiness of the child is explained by the number of siblings 65.47% of variation in happiness of the child is unexplained by the number of siblings

( f )