The Times-Observer is a daily newspaper in Metro City. Like many city newspapers

Question

The Times-Observer is a daily newspaper in Metro City. Like many city newspapers, the Times-Observer is suffering through difficult financial times. The circulation manager is studying other newspapers in similar cities in the United States and Canada. She is particularly interested in what variables relate to the number of subscriptions to the newspaper. She is able to obtain information on 25 newspapers in similar cities. The following notation is used:

                Sub = Number of subscriptions (in thousands)

                Popul = The metropolitan population (in thousands)

                Adv = The advertising budget of the newspaper (in $ hundreds)

                Income = The median family income in the metropolitan area (in $ thousands)

Develop a multiple regression equation with Sub as the dependent variable.

At the 0.10 level of significance, can you say that the effect of Income on the number of subscriptions is significantly different from zero? Why or why not?

Estimate the change in subscriptions in thousands (Sub) if the advertising budget (Adv) increases by $5,000 (change in Adv = 50).

Sub Popul Adv Income 37.95 588.9 13.2 35.1 37.66 585.3 13.2 34.7 37.55 566.3 19.8 34.8 38.78 642.9 17.6 35.1 37.67 624.2 17.6 34.6 38.23 603.9 15.4 34.8 36.9 571.9 11 34.7 38.28 584.3 28.6 35.3 38.95 605 28.6 35.1 39.27 676.3 17.6 35.6 38.3 587.4 17.6 34.9 38.84 576.4 22 35.4 38.14 570.8 17.6 35 38.39 586.5 15.4 35.5 37.29 544 11 34.9 39.15 611.1 24.2 35 38.29 643.3 17.6 35.3 38.09 635.6 19.8 34.8 37.83 598.9 15.4 35.1 39.37 657 22 35.3 37.81 595.2 15.4 35.1 37.42 520 19.8 35.1 38.83 629.6 22 35.3 38.33 680 24.2 34.7 40.24 651.2 33 35.8

Explanation / Answer

Regression Analysis: Sub versus Popul, Adv, Income

Analysis of Variance

Source        DF Adj SS    Adj MS    F-Value P-Value
Regression 3    11.191    3.7303    32.68    0.000
Popul       1    1.695    1.6948    14.85    0.001
Adv                1    3.459    3.4590    30.30    0.000
Income       1    2.472 2.4720    21.65    0.000
Error              21    2.397 0.1142
Total         24 13.588

Model Summary

       S          R-sq       R-sq(adj)     R-sq(pred)
0.337871    82.36%     79.84%      20.88%

Coefficients

Term           Coef       SE Coef    T-Value P-Value   VIF
Constant     -5.63     8.71      -0.65       0.525
Popul       0.002251 0.000584     3.85        0.001    1.05
Adv              0.0788         0.0143         5.50      0.000    1.30
Income        1.172            0.252    4.65   0.000    1.24

Regression Equation

Sub = -5.63 + 0.002251 Popul + 0.0788 Adv + 1.172 Income

sub = -5.63 + 0.002251 Popul + 0.0788 Adv + 1.172 *50

sub = 52.97 + 0.002251 Popul + 0.0788 Adv

Lower 99.0% Upper 99.0% -30.28553724 19.0323748 0.000596829 0.003904694 0.038292434 0.119407144 0.458781813 1.884607716

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.