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 cars’ average Speed was 26.38 mph, with standard deviation of 9.68 mph. These researchers found the regression line for these data to be S p e e d ^ = 50.55 − 0.352 D e n s i t y . 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 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 measured the Speed of the cars in kilometers per hour (1 km ≈ 0.62 miles) and the traffic Density in cars per kilometer. Find the value of his calculated correlation between speed and density.
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 cars’ average Speed was 26.38 mph, with standard deviation of 9.68 mph. These researchers found the regression line for these data to be S p e e d ^ = 50.55 − 0.352 D e n s i t y . 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 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 measured the Speed of the cars in kilometers per hour (1 km ≈ 0.62 miles) and the traffic Density in cars per kilometer. Find the value of his calculated correlation between speed and density.
Solution Summary: The author explains how the correlation coefficient between speed and density is –0.984.
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 cars’ average Speed was 26.38 mph, with standard deviation of 9.68 mph. These researchers found the regression line for these data to be
S
p
e
e
d
^
=
50.55
−
0.352
D
e
n
s
i
t
y
.
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 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 measured the Speed of the cars in kilometers per hour (1 km ≈ 0.62 miles) and the traffic Density in cars per kilometer. Find the value of his calculated correlation between speed and density.
Definition Definition Statistical measure used to assess the strength and direction of relationships between two variables. Correlation coefficients range between -1 and 1. A coefficient value of 0 indicates that there is no relationship between the variables, whereas a -1 or 1 indicates that there is a perfect negative or positive correlation.
08:34
◄ Classroom
07:59
Probs. 5-32/33
D
ا.
89
5-34. Determine the horizontal and vertical components
of reaction at the pin A and the normal force at the smooth
peg B on the member.
A
0,4 m
0.4 m
Prob. 5-34
F=600 N
fr
th
ar
0.
163586
5-37. The wooden plank resting between the buildings
deflects slightly when it supports the 50-kg boy. This
deflection causes a triangular distribution of load at its ends.
having maximum intensities of w, and wg. Determine w
and wg. each measured in N/m. when the boy is standing
3 m from one end as shown. Neglect the mass of the plank.
0.45 m
3 m
Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include:
Mileage (mpg)
Number of Cylinders (cyl)
Displacement (disp)
Horsepower (hp)
Research: Google to understand these variables.
Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp
Mean
Median
First Quartile (Q1)
Second Quartile (Q2)
Third Quartile (Q3)
Fourth Quartile (Q4)
10th Percentile
70th Percentile
Skewness
Kurtosis
Document Your Results:
In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command”
In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…
Examine the Variables: Carefully review and note the names of all variables in the dataset. Examples of these variables include:
Mileage (mpg)
Number of Cylinders (cyl)
Displacement (disp)
Horsepower (hp)
Research: Google to understand these variables.
Statistical Analysis: Select mpg variable, and perform the following statistical tests. Once you are done with these tests using mpg variable, repeat the same with hp
Mean
Median
First Quartile (Q1)
Second Quartile (Q2)
Third Quartile (Q3)
Fourth Quartile (Q4)
10th Percentile
70th Percentile
Skewness
Kurtosis
Document Your Results:
In RStudio: Before running each statistical test, provide a heading in the format shown at the bottom. “# Mean of mileage – Your name’s command”
In Microsoft Word: Once you've completed all tests, take a screenshot of your results in RStudio and paste it into a Microsoft Word document. Make sure that snapshots are very clear. You will need multiple snapshots. Also transfer these results to the…
Chapter R Solutions
Intro Stats, Books a la Carte Edition (5th Edition)
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