3. Urban economies resited The data set on urban economies used for home- work 3

Question

3. Urban economies resited The data set on urban economies used for home- work 3 contains, in addition to the per-capita gross metropolitan product (in dollars per person per year) and the population of each city, the frac tion (not percentage) of each city's economy devoted to four industries finance, "professional and technical" services, information and communi cations technologies (ICT), and management services. Here is the sum- mary of a linear model fit to this data Call: lm (formula = pcgmp ~ . - MSA, data- bea) Residuals: Min 1Q Median 3Q Max 806 3087 25556 19160 -4813 Coefficients: Estimate Std. Error t value Pr(>ltl) (Intercept) 2.17e+04 1.88e+03 11.52

Explanation / Answer

a) The estiamted regression equation is
y = 2.17e+04 + 2.24e-03 pop + 2.24e+04finance + 3.09e+04prof.tech + 6.42e+04ict + 1.95e+05 management

b) Root mean squared error is 7250

c) P-value of Prof.tech > alpha 0.05, so there is no significant
that means, the population regression coefficient is zero

d) The 95% confidence interval of the regression coeffient of prof.tech is
3.09e+4 - 1.9789*3.75e+04 = -43308.75
3.09e+4 + 1.9789*3.75e+04 = 105108.8

e)the population regression coefficient is zero i.e. not significant
since 0 is lies in the confidence interval

f)The estiamted regression equation is
y = 2.17e+04 + 2.24e-03 *236100 + 2.24e+04*0.2018 + 3.09e+04*0.0777 + 6.42e+04*0.03434 + 1.95e+05 *0.02946
=37099.44

g) P-value of Pittsburgh is > 0.05, so there is no significant
that means,the regression equation is not best fit of the given data

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