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Analyzing Magazine Circulation: Correlation and Prediction from Pricing Data

This review explores the relationship between the price of a magazine issue and its monthly circulation, using statistical methods to calculate the correlation coefficient, the least-squares prediction equation, and the predicted circulation at a specific price point. We assess the significance of the correlation and provide a predictive interval for the magazine's circulation based on pricing. Utilizing the dataset, we derive critical values and interpret the results that showcase the impact of pricing on readership. Homework assignments are included for further practice.

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Analyzing Magazine Circulation: Correlation and Prediction from Pricing Data

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  1. Advanced Math Topics Chapter 11 Review

  2. A magazine publisher has determined that the monthly circulation of the magazine depends upon the price charged per issue as shown below: 10 Find: Σ x = Σ y = Σ x2 = Σ y2 = Σ xy = x = n = 253 11,065 18.125 398 1.6667 6

  3. 1) Compute the coefficient of correlation for this data. Cox loves willis!!!! And schembri and finegold! Hey class! r = -0.9838

  4. 2) Is r significant? The critical r from the back of the book for n = 6 and r0.025 is + or -0.811. The computed r from the last slide is outside the region (closer to 1 or -1), so the correlation coefficient is significant.

  5. 3) Find the least-squares prediction equation. = 69.2143 = -16.2286 y = -16.2286x + 69.2143

  6. 4) If the magazine is priced to sell at $2.25, what is its predicted circulation? y = -16.2286(2.25) + 69.2143 y = 32.7000 which stands for 32,700 newspapers. If this number is used again, use 32.7000.

  7. 5) What is the value of the standard error of the estimate? = 1.7864

  8. 6) At the 5% level of significance, does the data indicate that the price charged per issue can be used as a predictor of its circulation? Find the critical t and calculate t. t = 10.9706 t0.025 with df = 4. The critical t-value is + or – 2.776. Since t is outside the interval, we reject that the slope is 0. Thus, the price is a predictor of circulation.

  9. 7) Find a 95% prediction interval for the circulation, in thousands, for the price per issue of $2.25. 26.8329 to 38.5671 thousand papers.

  10. HW: P. 593 #4, 6, 7, 12, 13 Please check your answers (evens and odds) in the back of the book Possible Jury Duty Tomorrow

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