Internet Advertising Several months ago, John O'Hagan investigated the effect on the popularity of OHaganBooks.com of placing banner ads at well-known Internet portals. The following model was obtained from available data:
a. John O’Hagan is considering increasing expenditure on banner ads from the current level of $5,000 to $6,000 per month. What will be the resulting effect on website popularity?
b. According to the model, would the website popularity continue to grow at the same rate if he continued to raise expenditure on advertising $1,000 each month? Explain.
c. Does this model give a reasonable prediction of traffic at expenditures larger than $8,500 per month? Why or why not?
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Chapter 1 Solutions
Finite Mathematics
- The U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below. The current minimum wage is $5.15. If an employee earns the minimum wage, how many complaints can that employee expect to receive? Is the regression coefficient statistically significant? How can you tell?arrow_forwardThe U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below. What proportion of variation in the number of complaints can be explained by hourly wages? From the results shown above, write the regression equation If wages were increased by $1.00, what is the expected effect on the number of complaints received per employee?arrow_forwardThe November 24, 2001, issue of The Economist published economic data for 15 industrialized nations. Included were the percent changes in gross domestic product (GDP), industrial production (IP), consumer prices (CP), and producer prices (PP) from Fall 2000 to Fall 2001, and the unemployment rate in Fall 2001 (UNEMP). An economist wants to construct a model to predict GDP from the other variables. A fit of the model GDP = , + P,IP + 0,UNEMP + f,CP + P,PP + € yields the following output: The regression equation is GDP = 1.19 + 0.17 IP + 0.18 UNEMP + 0.18 CP – 0.18 PP Predictor Coef SE Coef тР Constant 1.18957 0.42180 2.82 0.018 IP 0.17326 0.041962 4.13 0.002 UNEMP 0.17918 0.045895 3.90 0.003 CP 0.17591 0.11365 1.55 0.153 PP -0.18393 0.068808 -2.67 0.023 Predict the percent change in GDP for a country with IP = 0.5, UNEMP = 5.7, CP = 3.0, and PP = 4.1. a. b. If two countries differ in unemployment rate by 1%, by how much would you predict their percent changes in GDP to differ, other…arrow_forward
- Employment. According to the U.S. Bureau of Labor Statistics, the number of professional services employees fluctuated during the period 2000-2009, as modeled by E(t) = -28.31t³ +381.86t² - 1162.07t + 16,905.87, where t is the number of years since 2000 (t = 0 corresponds to 2000) and E is thousands of employees. (Source: www.data.bls.gov.) Find the relative extrema of this function, and sketch the graph. Interpret the meaning of the relative extrema.arrow_forwardA poultry raiser harvests an average of 300 eggs per day. He has recently experimented with the different types of poultry feeds. As a result, he noticed some fluctuation in the number of eggs laid by the chickens, which is neither clearly higher nor lower than previous weeks. He decides to find out whether there might be a significant change in the number of eggs laid by the chickens. He records his harvest of eggs for 20 days. He finds that the average per day is 290 eggs with a standard deviation of 15. At 5% level of significance, what did the poultry raiser find out?arrow_forwardA study was conducted to see if a person's income will affect their well-being. We want to create a model with Y = well-being index, and X = income in $1,000. The dependent variable in this study is: Income in $1,000 Well-being index Neitherarrow_forward
- The university wants to know if Annual Income and Lifetime Savings are linearly related. Investigate and state your answer with evidence. Does your answer seem logical or not? Write your thoughts on this.arrow_forwardIn a recent survey, ice cream truck drivers in Cincinnati, Ohio, reported they make about $280 in income on a typical summer day. The income was generally higher on days with longer work hours, particularly hot day, and on holidays. The IceCream data file includes five weeks of the driver's daily income (Income), number of hours on the road (Hours), whether it was a particularly hot day (Hot = 1 if the high temperature was above 85-degrees F, 0 otherwise), and whether it was a Holiday (Holiday = 1, 0 otherwise). 1. Predict the income of a driver working 8 hours on a hot holiday. (Round to the nearest dollar.) 2. Predict the income of a driver working 8 hours on a hot day if it was not a holiday. (Round to the nearest dollar.)arrow_forwardAn analyst in the real estate business is interested in the relationship between the cost of the monthly rent of an apartment and the size of an apartment, in big cities. She gathers data for apartment buildings in 12 cities in 12 different states. In each city, she gets the numbers for at least 5 different buildings and at least 40 apartments in each building. She reaches the following conclusion: the rental cost of a 2-bedroom apartment is 50% more than the rental cost of a 1-bedroom apartment, and the rental cost of a 3-bedroom apartment is 50% more than the rental cost of a 2-bedroom apartment. Based on the paragraph, what is the minimum number of apartments she collected data on? Do you think her sample was large enough to be statistically valid? Based on the paragraph, are there any apartments or apartment buildings that she would have excluded from her study? Do you see any bias in how she selected apartments for her study? Based on the paragraph, is there a positive…arrow_forward
- In linear regression analysis, the coefficient for the x-variable when the y-variable is regressed on the x-variable can be thought of as: Note: more than one answer may be correct Group of answer choices How much the value of the predicted y-variable will change when the x-variable changes by one unit. In the simple (two variable) linear regression model, the coefficient can be thought as the slope coefficient that measures the responsiveness of y to changes in x. The estimated coefficient will change if the sample containing x and y changes. The sample coefficient is an estimate of the population coefficient Before interpreting the coefficient for the x-variable, we should test whether the coefficient is statistically significant.arrow_forwardThe computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river. Which of the following statements is a correct interpretation of the value 19.0 in the output? On average there is a predicted increase of 19.0 ppm in concentration of lead for every increase of 1 ppm in concentration of zinc found in the fish. On average there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish. The predicted concentration of zinc is 19.0 ppm in fish with no concentration of lead. The predicted concentration of lead is 19.0 ppm in fish with no concentration of zinc. Approximately 19% of the variability in zinc concentration is predicted by its linear relationship with lead concentration.arrow_forwardThe county assessor is studying housing demand and is interested in developing a regression model to estimate the market value (i.e., selling price) of residential property within her jurisdiction. The assessor suspects that the most important variable affecting selling price (measured in thousands of dollars) is the size of house (measured in hundreds of square feet). She randomly selects 15 houses and measures both the selling price and size, as shown in the following table. Complete the table and then use it to determine the estimated regression line. Observation i 1 2 3 4 5 6 7 8 9 10 i 11 12 13 14 15 Total O 8.074 Regression Parameters Slope (B) Intercept (α) 10.181 8.358 O 0.327 Size (x 100 sq. ft.) O 0.316 12 20.2 27 O 0.398 30 30 O Yes 21.4 21.6 25.2 37.2 14.4 15 22.4 23.9 26.6 30.7 357.60 O No What is the standard error of the estimate (Se)? In words, for each hundred square feet, the expected selling price of a house Selling Price (x $1,000) Ii Yi y 265.2 253.4 12 2 20.2…arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning