A researcher collected data on length at birth and the length at six months for eight infants.

1. a)(1)Assumethatwewishtopredicthowlonganinfantwillbeat6monthsbasedonitsbirth length. Which variable is the predictor (explanatory) variable and which variable is the response?
2. b)(2)Constructascatterplotofyversusx.Dothedataseemtofollowanapproximatelylinear relationship?
3. c)(5) Calculate the following values:?x,?x2,?y,?y2, and?xy.
4. d)(4) Using your answers to part (c), calculate SSxxand SSxy.
5. e)(2) Determine the LS estimate of the slope. Interpret the meaning of this value in terms of birth
6. length and 6-month length.
7. f)(2) Determine the LS estimate of they-intercept. Does it make practical sense to think of a
8. birth length of 0"?
9. g)(4)Foreachofthegivenobservationsinthedatatable,determinetheresidual.
10. h)(1)Fromtheresidualsinpart(g),calculatethesumofsquaredresiduals,SSE=?e2i.
11. i)(2) Using the shortcut formula, calculate SSE=SSyy-?^1SSxy. How does this answer compare

A researcher collected data on length at birth and the length at six months for eight infants. infant 1 2 3 4 5 6 7 8 birth length (inches) 19.75 20.5 19 21 19 18.5 20.25 20 6month length (inches) 25.5 26.25 25 26.75 25.75 25.25 27 26.5 a) (1) Assume that we wish to predict how long an infant will be at 6 months based on its birth length. Which variable is the predictor (explanatory) variable and which variable is the response? b) (2) Construct a scatter plot of y versus x. Do the data seem to follow an approximately linear relationship? c) (5) Calculate the following values: 2 x , Z x2 , 2 y , 2 y2 , and 2 xy . d) (4) Using your answers to part (c), calculate SSxx and SSxy. e) (2) Determine the LS estimate of the slope. Interpret the meaning of this value in terms of birth length and 6month length. f) (2) Determine the LS estimate of the yintercept. Does it make practical sense to think of a birth length of 0\"? g) (4) For each of the given observations in the data table, determine the residual. h) (1) From the residuals in part (g), calculate the sum of squared residuals, SSE = 2 e,-2 . i) (2) Using the shortcut formula, calculate SSE: SS yy Blssxy . How does this answer compare to part (h)