/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 13 a. The first scatterplot shows t... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 13

a. The first scatterplot shows the college tuition and percentage acceptance at some colleges in Massachusetts. Would it make sense to find the correlation using this data set? Why or why not? b. The second scatterplot shows the composite grade on the ACT (American College Testing) exam and the English grade on the same exam. Would it make sense to find the correlation using this data set? Why or why not?

Short Answer

Expert verified
Yes to both. It would make sense to find the correlation in both situations as it may provide valuable insight into the relationships between the variables. However, one must always keep in mind that correlation does not imply causation.

Step by step solution

01

Scenario A Analysis

Looking at the first scatterplot talks about the 'college tuition' and 'percentage acceptance' at colleges in Massachusetts. Correlation could be useful here if one is trying to determine whether the cost of tuition has a direct effect on the rate of acceptance to these colleges. However, remember that correlation does not imply causation, meaning that even if a correlation exists, there might not be a direct cause-and-effect relationship.
02

Scenario B Analysis

In the second scatterplot, the variables are the 'composite grade on the ACT exam' and the 'English grade on the same exam'. It might make sense to find the correlation here as well because these two variables could likely be related. A student who performs well on the ACT overall may be more likely to do well on the English section, and vice versa.

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Most popular questions from this chapter

The following table gives the number of millionaires (in thousands) and the population (in hundreds of thousands) for the states in the northeastern region of the United States in 2008 . The numbers of millionaires come from Forbes Magazine in March 2007 . a. Without doing any calculations, predict whether the correlation and slope will be positive or negative. Explain your prediction. b. Make a scatterplot with the population (in hundreds of thousands) on the \(x\) -axis and the number of millionaires (in thousands) on the \(y\) -axis. Was your prediction correct? c. Find the numerical value for the correlation. d. Find the value of the slope and explain what it means in context. Be careful with the units. e. Explain why interpreting the value for the intercept does not make sense in this situation. $$ \begin{array}{|l|c|r|} \hline \text { State } & \text { Millionaires } & \text { Population } \\ \hline \text { Connecticut } & 86 & 35 \\ \hline \text { Delaware } & 18 & 8 \\ \hline \text { Maine } & 22 & 13 \\ \hline \text { Massachusetts } & 141 & 64 \\ \hline \text { New Hampshire } & 26 & 13 \\ \hline \text { New Jersey } & 207 & 87 \\ \hline \text { New York } & 368 & 193 \\ \hline \text { Pennsylvania } & 228 & 124 \\ \hline \text { Rhode Island } & 20 & 11 \\ \hline \text { Vermont } & 11 & 6 \\ \hline \end{array} $$

Data on the number of home runs, strikeouts, and batting averages for a sample of 50 Major League Baseball players were obtained. Regression analyses were conducted on the relationships between home runs and strikeouts and between home runs and batting averages. The StatCrunch results are shown below. (Source: mlb.com) Simple linear regression results: Dependent Variable: Home Runs Independent Variable: Strikeouts Home Runs \(=0.092770565+0.22866236\) Strikeouts Sample size: 50 \(\mathrm{R}\) (correlation coefficient) \(=0.63591835\) \(\mathrm{R}-\mathrm{sq}=0.40439215\) Estimate of error standard deviation: \(8.7661607\) Simple linear regression results: Dependent Variable: Home Runs Independent Variable: Batting Average Home Runs \(=45.463921-71.232795\) Batting Average Sample size: 50 \(\mathrm{R}\) (correlation coefficient) \(=-0.093683651\) \(\mathrm{R}-\mathrm{sq}=0.0087766264\) Estimate of error standard deviation: \(11.30876\) Based on this sample, is there a stronger association between home runs and strikeouts or home runs and batting average? Provide a reason for your choice based on the StatCrunch results provided.

The data shows the number of calories, carbohydrates (in grams) and sugar (in grams) found in a selection of menu items at McDonald's. Scatterplots suggest the relationship between calories and both carbs and sugars is linear. The data are also available on this text's website. (Source: shapefit.com) $$ \begin{array}{|c|c|c|} \hline \text { Calories } & \text { Carbs (in grams) } & \text { Sugars (in grams) } \\ \hline 530 & 47 & 9 \\ \hline 520 & 42 & 10 \\ \hline 720 & 52 & 14 \\ \hline 610 & 47 & 10 \\ \hline 600 & 48 & 12 \\ \hline 540 & 45 & 9 \\ \hline 740 & 43 & 10 \\ \hline 240 & 32 & 6 \\ \hline 290 & 33 & 7 \\ \hline 340 & 37 & 7 \\ \hline 300 & 32 & 6 \\ \hline 430 & 35 & 7 \\ \hline 380 & 34 & 7 \\ \hline 430 & 35 & 6 \\ \hline 440 & 35 & 7 \\ \hline 430 & 34 & 7 \\ \hline 750 & 65 & 16 \\ \hline 590 & 51 & 14 \\ \hline 510 & 55 & 10 \\ \hline 350 & 42 & 8 \\ \hline \end{array} $$ $$ \begin{array}{|l|l|} \hline \text { Calories } & \text { Carbs (in grams) } & \text { Sugars (in grams) } \\ \hline 670 & 58 & 11 \\ \hline 510 & 44 & 9 \\ \hline 610 & 57 & 11 \\ \hline 450 & 43 & 9 \\ \hline 360 & 40 & 5 \\ \hline 360 & 40 & 5 \\ \hline 430 & 41 & 6 \\ \hline 480 & 43 & 6 \\ \hline 430 & 43 & 7 \\ \hline 390 & 39 & 5 \\ \hline 500 & 44 & 11 \\ \hline 670 & 68 & 12 \\ \hline 510 & 54 & 10 \\ \hline 630 & 56 & 7 \\ \hline 480 & 42 & 6 \\ \hline 610 & 56 & 8 \\ \hline 450 & 42 & 6 \\ \hline 540 & 61 & 14 \\ \hline 380 & 47 & 12 \\ \hline 340 & 37 & 8 \\ \hline 260 & 30 & 7 \\ \hline 340 & 34 & 5 \\ \hline 260 & 27 & 4 \\ \hline 360 & 32 & 3 \\ \hline 280 & 25 & 2 \\ \hline 330 & 26 & 3 \\ \hline 190 & 12 & 0 \\ \hline 750 & 65 & 16 \\ \hline \end{array} $$ a. Calculate the correlation coefficient and report the equation of the regression line using carbs as the predictor and calories as the response variable. Report the slope and interpret it in the context of this problem. Then use your regression equation to predict the number of calories in a menu item containing 55 grams of carbohydrates. b. Calculate the correlation coefficient and report the equation of the regression line using sugar as the predictor and calories as the response variable. Report the slope and interpret it in the context of this problem. Then use your regression equation to predict the number of calories in a menu item containing 10 grams of sugars. c. Based on your answers to parts (a) and (b), which is a better predictor of calories for these data: carbs or sugars? Explain your choice using appropriate statistics.

Move studios try to predict how much money their movies will make. One possible predictor is the amount of money spent on the production of the movie. The table shows the budget and amount of money made for a sample of movies made in 2017 . The budget (amount spent making the movie) and gross (amount earned by ticket sales) are shown in the table. Make a scatterplot of the data and comment on what you see. If appropriate, do a complete linear regression analysis. If it is not appropriate to do so, explain why not. (Source: IMDB) $$ \begin{array}{|lcc|} \hline \text { Film } & \begin{array}{c} \text { Gross(in \$ } \\ \text { millions) } \end{array} & \begin{array}{c} \text { Budget (in \$ } \\ \text { millions) } \end{array} \\ \hline \text { Wonder Woman } & 412.6 & 149 \\ \hline \text { Beauty and the Beast } & 504 & 160 \\ \hline \text { Guardians of the Galaxy Vol. } 2 & 389.8 & 200 \\ \hline \text { Spider-Man: Homecoming } & 334.2 & 175 \\ \hline \text { It } & 327.5 & 35 \\ \hline \text { Despicable Me 3 } & 264.6 & 80 \\ \hline \text { Logan } & 226.3 & 97 \\ \hline \text { The Fate of the Furious } & 225.8 & 250 \\ \hline \text { Dunkirk } & 188 & 100 \\ \hline \text { The LEGO Batman Movie } & 175.8 & 80 \\ \hline \text { Thor Ragnarok } & 310.7 & 180 \\ \hline \text { Get Out } & 175.5 & 5 \\ \hline \text { Dead Men Tell No Tales } & 172.6 & 230 \\ \hline \text { Cars } 3 & 152 & 175 \\ \hline \end{array} $$

Some investors use a technique called the "Dogs of the Dow" to invest. They pick several stocks that are performing poorly from the Dow Jones group (which is a composite of 30 wellknown stocks) and invest in these. Explain why these stocks will probably do better than they have done before.
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