Traffic Highway planners investigated the relationshipbetween traffic Density (number of automobiles per mile)and the average Speed of the traffic on a moderately largecity thoroughfare. The data were collected at the samelocation 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 Speed = 50.55 - 0.352 Density.a) What is the value of the correlation coefficientbetween Speed and Density?b) What percent of the variation in average Speed isexplained by traffic Density? c) Predict the average Speed of traffic on the thorough-fare when the traffic Density is 50 cpm. d) What is the value of the residual for a traffic Densityof 56 cpm with an observed Speed of 32.5 mph?e) The data set initially included the point Density =125 cpm, Speed = 55 mph. This point was consideredan outlier and was not included in the analysis. Willthe slope increase, decrease, or remain the same if weredo the analysis and include this point?f) Will the correlation become stronger, weaker, orremain the same if we redo the analysis and includethis point (125,55)? g) A European member of the research team mea-sured the Speed of the cars in kilometers per hour 11 km ≈ 0.62 miles2 and the traffic Density in cars per kilometer. Find the value of his calculated correla-tion between speed and density.
Traffic Highway planners investigated the relationshipbetween traffic Density (number of automobiles per mile)and the average Speed of the traffic on a moderately largecity thoroughfare. The data were collected at the samelocation 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 Speed = 50.55 - 0.352 Density.a) What is the value of the correlation coefficientbetween Speed and Density?b) What percent of the variation in average Speed isexplained by traffic Density? c) Predict the average Speed of traffic on the thorough-fare when the traffic Density is 50 cpm. d) What is the value of the residual for a traffic Densityof 56 cpm with an observed Speed of 32.5 mph?e) The data set initially included the point Density =125 cpm, Speed = 55 mph. This point was consideredan outlier and was not included in the analysis. Willthe slope increase, decrease, or remain the same if weredo the analysis and include this point?f) Will the correlation become stronger, weaker, orremain the same if we redo the analysis and includethis point (125,55)? g) A European member of the research team mea-sured the Speed of the cars in kilometers per hour 11 km ≈ 0.62 miles2 and the traffic Density in cars per kilometer. Find the value of his calculated correla-tion between speed and density.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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Question
Traffic 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
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
tion of 9.68 mph. These researchers found the regression
line for these data to be Speed = 50.55 - 0.352 Density.
a) What is the value of thecorrelation coefficient
between Speed and Density?
b) What percent of the variation in average Speed is
explained by traffic Density?
a) What is the value of the
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 thorough-
fare when the traffic Density is 50 cpm.
fare 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 Density =
125 cpm, Speed = 55 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)?
of 56 cpm with an observed Speed of 32.5 mph?
e) The data set initially included the point Density =
125 cpm, Speed = 55 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 mea-
sured the Speed of the cars in kilometers per hour
sured the Speed of the cars in kilometers per hour
11 km ≈ 0.62 miles2 and the traffic Density in cars
per kilometer. Find the value of his calculated correla-
tion between speed and density.
tion between speed and density.
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