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In: Math

Consider the following table summarizing the speed limit of a certain road and the number of...

Consider the following table summarizing the speed limit of a certain road and the number of accidents occurring on that road in January. Posted Speed Limit 52 50 43 36 21 22. Reported Number of Accidents 27 26 23 18 18 11. 1) Find the slope of the regression line predicting the number of accidents from the posted speed limit.Round to 3 decimal places. 2) Find the intercept of the regression line predicting the number of accidents from the posted speed limit. Round to 3 decimal places. 3) Predict the number of reported accidents for a posted speed limit of 25mph. Round to the nearest whole number.

Solutions

Expert Solution

Consider the following table summarizing the speed limit of a certain road and the number of accidents occurring on that road in January. Posted Speed Limit 52 50 43 36 21 22. Reported Number of Accidents 27 26 23 18 18 11.

Find the slope of the regression line predicting the number of accidents from the posted speed limit.Round to 3 decimal places.

Slope= 0.405

2) Find the intercept of the regression line predicting the number of accidents from the posted speed limit. Round to 3 decimal places.

Intercept=5.384

3) Predict the number of reported accidents for a posted speed limit of 25mph. Round to the nearest whole number.

The estimated regression line is number of accidents =5.384+0.405*speed limit

When speed limit is 25,

Predicted number of accidents =5.384+0.405*25=15.509

=16 ( rounded)

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis

Regression Analysis

r²

0.823

n

6

r

0.907

k

1

Std. Error of Estimate

2.832

Dep. Var.

Number of Accidents

Regression output

confidence interval

variables

coefficients

std. error

   t (df=4)

p-value

95% lower

95% upper

Intercept

a =

5.384

Speed

b =

0.405

0.094

4.315

.0125

0.144

0.665

ANOVA table

Source

SS

df

MS

F

p-value

Regression

149.409

1   

149.409

18.62

.0125

Residual

32.091

4  

8.023

Total

181.500

5  

Predicted values for: Number of Accidents

95% Confidence Interval

95% Prediction Interval

Speed

Predicted

lower

upper

lower

upper

Leverage

25

15.51

10.96

20.05

6.42

24.59

0.334

milcah answered 1 year ago
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