Answered: You are given the following data, where…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

Problem 6E: Urban Travel Times Population of cities and driving times are related, as shown in the accompanying...

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This problem is based on problems 18.1, 18.2, 18.9, & 18.10 from Lomax & Hahs-Vaughn, 3rd ed.

You are given the following data, where X1X1 (years of working experience at current position) and X2X2 (salary in thousands) are used to predict YY (morale):

YY	X1X1	X2X2
170	7	49
130	2	30
195	9	56
185	3	31
180	10	52
175	9	53
160	6	49
165	5	48
115	4	45
150	4	42

Determine the following multiple regression values.

Report intercept and slopes for regression equation accurate to 3 decimal places:
    Intercept:  a=a=
    Partial slope X1X1:  b1=b1=
    Partial slope X2X2:  b2=b2=

Report sum of squares accurate to 3 decimal places:
    SSreg=SSreg=
    SSTotal=SSTotal=

Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places):
    F-ratio =
    P-value =

Report the variance of the residuals accurate to 3 decimal places:
    s2res=sres2=

Report the results for the hypothesis test for the significance of the partial slope for salary (report the test statistic for the regression coefficients accurate to 3 decimal places and P-value accurate to 4 decimal places):
    t2=t2=
    P-value =

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Urban Travel Times Population of cities and driving times are related, as shown in the accompanying table, which shows the 1960 population N, in thousands, for several cities, together with the average time T, in minutes, sent by residents driving to work. City Population N Driving time T Los Angeles 6489 16.8 Pittsburgh 1804 12.6 Washington 1808 14.3 Hutchinson 38 6.1 Nashville 347 10.8 Tallahassee 48 7.3 An analysis of these data, along with data from 17 other cities in the United States and Canada, led to a power model of average driving time as a function of population. a Construct a power model of driving time in minutes as a function of population measured in thousands b Is average driving time in Pittsburgh more or less than would be expected from its population? c If you wish to move to a smaller city to reduce your average driving time to work by 25, how much smaller should the city be?

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