Question

Measurements of length and weight for a sample of 20 low birth weight infants are contained in the data set twenty. The length measurements are saved under the variable name length, and the corresponding birth weights under weight.

(a) Construct a two-way scatter plot of birth weight versus length for the 20 infants in the sample. Without doing any calculations, sketch your best guess for the least-squares regression line directly on the scatter plot.

(b) Now compute the true least-squares regression line. Draw this line on the scatter plot. Does the actual least-squares line concur with your guess? Based on the two-way scatter plot, it is clear that one point lies outside the range of the remainder of the data. This point corresponds to the ninth infant in the sample of size 20. To illustrate the effect that the outlier has on the model, remove this point from the data set.

(c) Compute the new least-squares regression line based on the sample of size 19, and sketch this line on the original scatter plot. How does the least-squares line change? In particular, comment on the values of the slope and the intercept.

(d) Compare the coefficients of determination (R2) and the standard deviations from regression (sylx) for the two least-squares regression lines. Explain how these values changed when you removed the outlier from the original data set. Why did they change?

length	weight
41	1360
40	1490
38	1490
38	1180
38	1200
32	680
33	620
38	1060
30	1320
34	830
32	880
39	1130
38	1140
39	1350
37	950
39	1220
38	980
42	1480
39	1250
38	1250

*data in a copiable format

Answer 1