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 TimesObserver is suffering through difficult financial times. The circulation manager is studying other papers in similar cities in the United States and Canada. She is particularly interested in what variables relate to the number of subscriptions to the paper. She is able to obtain the following sample information on 25 newspapers in similar cities.

g. What is the standard error? Describe what this means as related to the problem.

h. For your initial model equation, discuss whether R2 or Adjusted R2 should be used in interpreting how good the linear equation is. Then, interpret the appropriate R2 value.

i. What does the overall statistical significance explain with respect to the model?

j. Evaluate the p-value for each independent variable. Should any of the independent variables be dropped? Why or why not?

k. Develop a correlation matrix for the independent variables. Should any of the independent variables be dropped? Why or why not?

l. Is this a good model?

Subscriptions Population Adv Income 38.95 588.90 13.06 33.51 37.66 585.30 13.24 33.63 38.55 566.30 13.43 33.68 38.78 642.90 13.61 33.75 38.67 624.20 13.99 33.86 38.23 603.90 14.18 33.90 37.90 571.90 14.86 34.05 38.28 584.30 17.64 34.11 38.95 605.00 17.72 34.17 40.27 676.30 17.73 34.21 39.30 587.40 18.20 34.25 38.84 576.40 18.53 34.27 38.14 570.80 19.82 34.45 39.39 586.50 20.24 34.66 38.29 544.00 20.94 34.72 39.15 611.10 21.38 34.84 38.29 643.30 21.61 34.88 38.09 635.60 21.68 35.20 37.83 598.90 21.70 35.26 39.37 657.00 22.35 35.44 37.81 595.20 23.41 35.72 38.42 520.00 23.69 35.76 38.83 629.60 23.81 35.81 39.33 680.00 25.39 35.85 41.24 651.20 25.92 35.87

Explanation / Answer

Using the simple regression model we can solve all the question bu using excel

g. the standard error is 0.6826 which tells us that the average distance of the data points from the fitted line is about 0.68

h. R2 = 0.377. We can say that 37.7% of the variation in the Subscriptions is reduced by taking into account all variables. NO, this value donot show your model is linear.

i. Population p-value is significant the Subscriptions variable where as others p-value is greater than 0.05.

SUMMARY OUTPUT Regression Statistics Multiple R 0.614226 R Square 0.377274 Adjusted R Square 0.288313 Standard Error 0.682657 Observations 25 ANOVA df SS MS F Significance F Regression 3 5.929034 1.976345 4.2409 0.017179 Residual 21 9.786422 0.46602 Total 24 15.71546 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 66.65939 21.17942 3.147367 0.004861 22.61438 110.7044 Population 0.010172 0.003622 2.808427 0.010529 0.00264 0.017705 Adv 0.243231 0.131248 1.85322 0.077955 -0.02971 0.516176 Income -1.1182 0.683654 -1.63562 0.116821 -2.53993 0.303539

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