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QUESTION:

Highway planners investigated the relationship between traffic Density (number of automobiles per mile) and the average Speed of the traffic on a moderately large city thoroughfare. The data were collected at the same location at 10 different times over a span of 3 months. They found a mean traffic Density of 68.6 cars per mile (cpm) with standard deviation of 27.07 cpm. Overall, the cars’ average Speed was 26.38 mph, with standard devia- tion of 9.68 mph. These researchers found the regression line for these data to be \(\widehat{\text { Speed }}=50.55-0.352\) Density.

a) What is the value of the correlation coefficient between Speed and Density?

b) What percent of the variation in average Speed is explained by traffic Density?

c) Predict the average Speed of traffic on the thoroughfare when the traffic Density is 50 cpm.

d) What is the value of the residual for a traffic Density of 56 cpm with an observed Speed of 32.5 mph?

e) The data set initially included the point \(\text { Density }=125 \mathrm{cpm}, \text { Speed }=55 \mathrm{mph}\). This point was considered an outlier and was not included in the analysis. Will the slope increase, decrease, or remain the same if we redo the analysis and include this point?

f) Will the correlation become stronger, weaker, or remain the same if we redo the analysis and include this point ( 125, 55 )?

g) A European member of the research team measured the Speed of the cars in kilometers per hour (\(1 \mathrm{~km} \approx 0.62 \text { miles }\)) and the traffic Density in cars per kilometer. Find the value of his calculated correla- tion between speed and density.