Week4 homework
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\f(c) For which data set is the sample correlation coefficient r closest to 0? l(Choose one} V l (d) For which data set is the sample correlation coefficient r equal to 1? \"Choose one) 7 Answer the following questions about the relationships between pairs of variables and the values of 1', the sample correlation coefficient. The same response may be the correct answer for more than one question. (a) Which data set indicates the strongest positive linear relationship between its two variables? X '53 I (Choose one) 7 | (b) For which data set is the sample correlation coefficient r closest to 1? I (Choose one} 7 | (c) For which data set is the sample correlation coefficient r closest to 0? Below are four bivariate data sets and their scatter plots. (Note that all of the scatter plots are displayed with the same scale. ) Each data set is made up of sample values drawn from a population. X y 11- V 11- 1.0 3.9 10- 1.0 3.7 10- x x x 2.0 6.1 X X 2.0 9- X 8- 6.5 X X 8- X 3.0 6.7 X X 3.0 8.3 4.0 4.3 X X X X 4.0 9.6 X 5.0 5.1 4 X X 5.0 9.9 X 6.0 8.5 3- 6.0 10.2 X 3- 7.0 5.5 7.0 9.1 8.0 7.3 8.0 8.5 9.0 8.9 2345 9.0 6.8 10.0 7.6 Figure 1 10.0 4.2 Figure 2\fthe two variables? I [Choose one} 1' (c) Which data set has an apparent positiveI but not perfect, linear relationship between its two variables? I (Choose one} 1 (d) Which data set indicates a perfect negative linear relationship between its two variables? I (Choose one) 1' Answer the Following questions. The same response may be the correct answer For more than one question. (a) Which data set indicates the strongest positive linear relationship between its two variables? X |(Choose one) V | (b) In which data set is there evidence of a strong nonlinear relationship between the two variables? |(Choose one) 7 (c) Which data set has an apparent positive, but not perfect, linear relationship between its two variables? \fAn advertising rm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (in millions of dollars) and the resulting percentage increase in sales following the campaign, were presented by the firm. Based on these data, we would compute the A least-squares regression line to be y = 6.19+ 0.173;, with 3: representing campaign cost and _1-' representing the resulting percentage increase in sales. (This line is shown below, along with a scatter plot of the data.) Campaign cost, x Increase in sales, y (in millions of dollars) (percent) se in sales Based on the rm's data and the regression line, complete the following. (a) For these data, values for percentage increase in sales that are less than the mean of the values for percentage increase in sales tend to be paired with values for campaign cost that are l {Choose one) 1 l the mean of the values for campaign cost. (b) According to the regression equation, for an increase of one million dollars in advertising campaign cost, there is a corresponding increase of hov.r many percent in sales? D Theater revenue, x Rental revenue, y (in millions of dollars) (in millions of dollars) 13 Rental revenue (in millions of dollars) 40- 35- X X X Xx 30- X Used selling price (in thousands of dollars) X X X X 25- X 20_ X 15 20 25 30 35 40 Mileage (in thousands)Ren (in milli m l Theater revenue (in millions of dollars) 13.1 i Send data to calculator v _I Based on the studio's data and the regression line, complete the following. Based on the studio's data and the regression line, complete the following. (a) For these data, values for rental revenue that are greater than the mean of the values for rental revenue tend to be paired with values for theater revenue that are |(Choose one) Y | the mean of the values for theater revenue. (b) According to the regression equation, for an increase of one million dollars in theater revenue, there is a corresponding increase of how many million dollars in rental revenue? D
