Chapter 12, Problem 12.21AC

Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300

XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?

Demand for Candy Bars In this problem you will determine a linear demand equation that describes the demand for candy bars in your class. Survey your classmates to determine what price they would be willing to pay for a candy bar. Your survey form might look like the sample to the left. a Make a table of the number of respondents who answered yes at each price level. b Make a scatter plot of your data. c Find and graph the regression line y=mp+b, which gives the number of respondents y who would buy a candy bar if the price were p cents. This is the demand equation. Why is the slope m negative? d What is the p-intercept of the demand equation? What does this intercept tell you about pricing candy bars? Would you buy a candy bar from the vending machine in the hallway if the price is as indicated. Price Yes or No 50 75 1.00 1.25 1.50 1.75 2.00

Johnson Filtration, Inc. provides maintenance service for water-filtration systems. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessarY, the managers obtained a list showing which repairperson performed the service. The revised data follow. Click on the datafile logo to reference the data. DATA file Repair Time Months Since in Hours Last Service Type of Repair Repairperson 2.9 Electrical Dave Newton 3.0 Mechanical Dave Newton 4.8 8. Electrical Bob Jones 1.8 3 Mechanical Dave Newton 2.9 2 Electrical Dave Newton 4.9 Electrical Bob Jones 4.2 6. Mechanical Bob Jones 4.8 8. Mechanical Bob Jones 4.4 Electrical Bob Jones 4.5 Electrical Dave Newton a. Ignore for now the months since the last maintenance service (1) and the repairperson who performed the service. Develop the estimated simple linear regression equation to predict the repair time (y) given the type of repair (2 ). Recall that…

An agent for a real estate company in a large city would like to be able to predict the monthly rental cost for apartments, based on the size of the apartment, as defined by square footage. A sample of eight apartments in a neighborhood was selected, and the information gathered revealed the data shown below. For these data, the regression coefficients are b, = 89.7175 and b, = 1.0703. Complete parts (a) through (d). Monthly Rent (S) Size (Square Feet) 900 1,450 850 1,500 2,000 900 1,825 1,300 o 850 1,350 950 1,200 1,900 700 1.350 1.050 ..... a. Determine the coefficient of determination, r, and interpret its meaning. 2= 0.843 (Round to three decimal places as needed.) What is the meaning of ? O A. r measures the proportion of variation in apartment size that can be explained by the variation in monthly rent. O B. r measures the proportion of variation in apartment size that cannot be explained by the variation in monthly rent. O C. measures the proportion of variation in monthly rent…

For Numbers 38 and 39: Suppose the tree's trunk diameter at breast height (DBH, in meters) can also be used to predict its weight. Hence, a multiple linear regression analysis was performed, and the results are as follows: Coefficients: *** A. 77.62 Estimate Sed. Erzort value Pr(it)) (Intercept) -1120.865 156.794 -7.149 0.000832 www. 39.803 204 571 5.140 0.003616 M 3.951 5-673 0.696 0.517252 0.01 *** OLOS - OLI A. 125.200 DBH Height 38. About % in the tree's weight can be explained by tree's height and trunk diameter at breast height. Signif. codes: TON -----0-001 Residual standard error; 125.2 on 5 degrees of freedom Multiple R-squared: 0.9688, Adjusted R-squared: 0-9563 F-statistic: 77.62 on 2 and 5 DE, p-value: 0.000172 B. 95.63 39. Suppose a tree was harvested and its height is equal to 50 ft. and its DBH is 7 m. The predicted weight of the tree using the estimated model is C. 96.88 B. 311.132 D. 125.2 C. 508.682 D. 1624.547

The following table gives the amount spent on cellular service.   Date Cellular service revenue(in billions) 2011 1.01 2012 1.05 2013 1.09 2014 1.11             Plot the data points. (Let tbe the number of years since 2011 and C the amount of cellular service revenue, in billions of dollars.)  CORRECT       (b) Find the equation of the regression line. (Let t be the number of years since 2011 and C the amount of cellular service revenue, in billions of dollars. Round the regression line parameters to three decimal places.) C(t) =  C(t) = 0.034t+1.014  CORRECT         Add its graph to the plotted data.          CORRECT   (c) In 2015, $1.14 trillion was spent on cellular service. If you had been a financial strategist in 2014 with only the data in the table above available, what would have been your prediction for the amount spent on cellular service in 2015? (Round your answer to two decimal places.) billion dollars  CORRECT…

To assess the relationship between monthly sales of a product and monthly advertising expenditure(both in thousands of dollars); a linear regression model was fitted using data for 20 months and results were as follows: s.e(8) Variable B Intercept 6.3812 advert 1.1762 0.0786 (a) From the results, we can say that an increase of 1000 dollars in monthly expenditure is associated with an increase of 1.1762 dollars in average sales. an increase of 1.1762 dollars in monthly expenditure is associated with an increase of one dollar in average selling price. an increase of 1000 dollars in monthly expenditure is associated with an increase of 1176.2 dollars in average sales. an increase of one dollar in monthly expenditure is associated with an increase of 1.1762 dollars in average sales. <

Define both x and y in all problems. x is the cause, and y is the effect. This is the most important step when doing linear regression, otherwise, all the remanding parts will be wrong.