Question

s (per 1 streets. speed s, in mdes per hour, for Explain what your answer means in practical terms Commercial vehicles driving at night on urban streets at

Answer 1

Here we will regress accident rate (R) with respect to speed s and s².

Here is the table and the screenshot of excel regression function.

Now here is the regression summary.

Book1 Microsoft Excel HomeInsert Page LayoutFormulas Data Review View Clear Data Analysis Properties Edit Links From From From From Other Existing Refresh Access Web Text SourcesConnections AlI Sort Filter y Text to Remove Data Consolidate What-If Group Ungroup Subtotal Advanced Columns Duplicates Validation Get External Data Connections Sort & Filter Data Tools 1 Speed (s) s 2 1650 2 sC$1:$C$7 InputRange: Labels Confidence Level: Constant is Zero 1300 Output optons O Qutput Range: New Worksheet Ply: O New Workbook Residuals □standardzed Residuals Residual Plots Dune Fit Plots 16 17 Normal Probablity Normal Probability Plots 19 H Sheet1 Sheet2 Sheet3 Ready 11:16 AM rP ^节口40) 4/9/2019 Type here to search

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.981256
R Square	0.962864
Adjusted R Square	0.938107
Standard Error	139.1299
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	2	1505679	752839.3	38.89207	0.007156
Residual	3	58071.43	19357.14
Total	5	1563750
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	8927.857	923.1084	9.671516	0.002347	5990.114	11865.6
Speed (s)	-524.786	59.57575	-8.80871	0.003083	-714.382	-335.189
s^2	7.928571	0.910819	8.704878	0.003191	5.029938	10.82721

Accident Rate (R) = 8927.86 - 524.79 s + 7.93 s²

(b) R(65) = 8927.86 - 524.79* 65  + 7.93 * 65 * 65 = 8315

Commercial vehicle driving at night on urban streets at 65 miles per hour have traffice accidents at a rate of 8500 per 100,000,000 vehicle miles.

(c) Here the accidents will be minimum when

dR/ds = 0

so here

dR/ds = -524.79 + 2 * 7.93 s = 0

s = 33.09 mph or 33 mph