find the regression? equation, letting the first variable be the predictor? (x)
ID: 2947646 • Letter: F
Question
find the regression? equation, letting the first variable be the predictor? (x) variable. Using the listed? lemon/crash data, where lemon imports are in metric tons and the fatality rates are per? 100,000 people, find the best predicted crash fatality rate for a year in which there are 525 metric tons of lemon imports. Is the prediction? worthwhile? Lemon Imports 226 270 354 483 544 Crash Fatality Rate 16 15.7 15.5 15.4 15 Find the equation of the regression line y = _ +? _x ?(Round the constant three decimal places as needed. Round the coefficient to six decimal places as needed.
The best predicted crash fatality rate for a year in which there are 525 metric tons of lemon imports is 15.1 fatalities per? 100,000 population.
?(Round to one decimal place as? needed.)
Is the prediction? worthwhile?
A.
Since all of the requirements for finding the equation of the regression line are? met, the prediction is worthwhile.
B.
Since the sample size is? small, the prediction is not appropriate.
C.
Since common sense suggests there should not be much of a relationship between the two? variables, the prediction does not make much sense.
D.
Since there appears to be an? outlier, the prediction is not appropriate.
Explanation / Answer
Result:
find the regression? equation, letting the first variable be the predictor? (x) variable. Using the listed? lemon/crash data, where lemon imports are in metric tons and the fatality rates are per? 100,000 people, find the best predicted crash fatality rate for a year in which there are 525 metric tons of lemon imports. Is the prediction? worthwhile?
LemonImports 226 270 354 483 544
CrashFatalityRate 16 15.7 15.5 15.4 15
Find the equation of the regression line
y = 16.490+( -0.002583)x
?(Round the constant three decimal places as needed. Round the coefficient to six decimal places as needed.
The best predicted crash fatality rate for a year in which there are 525 metric tons of lemon imports is 15.1 fatalities per? 100,000 population.
?(Round to one decimal place as? needed.)Is the prediction? worthwhile?
Answer: A.Since all of the requirements for finding the equation of the regression line are met, the prediction is worthwhile.
B.Since the sample size is? small, the prediction is not appropriate.
C.Since common sense suggests there should not be much of a relationship between the two? variables, the prediction does not make much sense.
D.Since there appears to be an? outlier, the prediction is not appropriate.
Regression Analysis
r²
0.899
n
5
r
-0.948
k
1
Std. Error
0.136
Dep. Var.
CrashFatalityRate
ANOVA table
Source
SS
df
MS
F
p-value
Regression
0.49288556
1
0.49288556
26.83
.0140
Residual
0.05511444
3
0.01837148
Total
0.54800000
4
Regression output
confidence interval
variables
coefficients
std. error
t (df=3)
p-value
95% lower
95% upper
Intercept
16.489552
0.1968
83.808
3.74E-06
15.8634
17.1157
LemonImports
-0.002583
0.00049863
-5.180
.0140
-0.0042
-0.0010
Predicted values for: CrashFatalityRate
95% Confidence Interval
95% Prediction Interval
LemonImports
Predicted
lower
upper
lower
upper
Leverage
525
15.1336
14.8277
15.4395
14.6048
15.6624
0.503
Regression Analysis
r²
0.899
n
5
r
-0.948
k
1
Std. Error
0.136
Dep. Var.
CrashFatalityRate
ANOVA table
Source
SS
df
MS
F
p-value
Regression
0.49288556
1
0.49288556
26.83
.0140
Residual
0.05511444
3
0.01837148
Total
0.54800000
4
Regression output
confidence interval
variables
coefficients
std. error
t (df=3)
p-value
95% lower
95% upper
Intercept
16.489552
0.1968
83.808
3.74E-06
15.8634
17.1157
LemonImports
-0.002583
0.00049863
-5.180
.0140
-0.0042
-0.0010
Predicted values for: CrashFatalityRate
95% Confidence Interval
95% Prediction Interval
LemonImports
Predicted
lower
upper
lower
upper
Leverage
525
15.1336
14.8277
15.4395
14.6048
15.6624
0.503
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