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Solutions to problems related to correlation and regression analysis. It includes the interpretation of scatterplots, calculation of correlation coefficients, and determination of regression lines. The document also discusses the impact of outliers and the use of the insight data point.

Typology: Assignments

Pre 2010

1 / 5

Download Analysis of Correlation and Regression: Homework Solutions and more Assignments Data Analysis & Statistical Methods in PDF only on Docsity! 1 Solutions: Homework 3, Supplemental Problems 2.14. (a) Below; speed is explanatory, so it belongs on the x-axis. (b) The relationship is curved low in the middle, higher at the extremes. Because low mileage is actually good (it means that we use less fuel to travel 100 km), this makes sense: moderate speeds yield the best performance. Note that 60 km/hr is about 37 mph. (Milage decreases until speed exceeds 60 km/h and then increases beyond that. 60 km/h is probably where the car shifts into high gear, which is more efficient. As speeds increase, wind resistance becomes more of a factor, causing fuel consumption to increase.) (c) Above-average (that is, bad) values of fuel used are found with both low and high values of speed. (d) The relationship is very strong there is little scatter around the curve, and it is very useful for prediction. It would appear that two lines (one for below 60 km/h and one above) would fit the data quite well. 0 50 100 150 5 10 15 20 Speed F ue l 2.32. See the solution to Exercise 2.14 for the scatterplot. r = 0.172 it is close to zero, because the relationship is a curve rather than a line; correlation measures the degree of linear association. 2.33. (a) The Insight seems to fit the line suggested by the other points. (b) Without the Insight, r = 0.9757; with it, r* = 0.9934. The Insight increases the strength of the association (the line is the same, but the scatter about that line is relatively less when the Insight is included). 2 10 20 30 40 50 60 10 20 30 40 50 60 70 City H w y 2.29. (a) The scatterplot shows a moderate positive association, so r should be positive, but not close to 1. (b) The correlation is r = 0.5653. (c) r would not change if all the men were six inches shorter. A positive correlation does not tell us that the men were generally taller than the women; instead it indicates that women who are taller (shorter) than the average woman tend to date men who are also taller (shorter) than the average man. (d) r would not change, because it is unaffected by units. (e) r would be 1, as the points of the scatterplot would fall on a positively-sloped line.