/*! 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} Q 70. Rushing for points What is the r... [FREE SOLUTION] | 91影视

91影视

Rushing for points What is the relationship between rushing yards and points scored in the National Football League? The table gives the number of rushing yards and the number of points scored for each of the 16 games played by the Jacksonville Jaguars in a recent season.

a. Make a scatterplot with rushing yards as the explanatory variable. Describe what you see.

b. The number of rushing yards in Game 16 is an outlier in the x-direction. What effect do you think this game has on the correlation? On the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this game to confirm your answers.

c. The number of points scored in Game 13 is an outlier in the y-direction. What effect do you think this game has on the correlation? On the equation of the least-squares regression line? Calculate the correlation and equation of the least-squares regression line with and without this game to confirm your answers.

Short Answer

Expert verified

Part (a) The scatterplot confirms a weak relationship because the points seem to lie far apart.

Part (b) The game 16makes the correlation increase.

Part (c) The game 13 makes the correlation decrease.

Step by step solution

01

Part (a) Step 1: Given information

02

Part (a) Step 2: Explanation

The scatterplot with rushing yards as the explanatory variable is as:

Because the scatterplot slopes upwards, we can conclude that the scatterplot confirms a positive linear connection. Because the points appear to be widely apart, the scatterplot indicates a weak association.

03

Part (b) Step 1: Explanation

For the case with outlier:

Using a calculator, press on STAT and then select 1 : Edit. and then enter the data of sugar in the list L1 and enter the data of calories in the list L2

Next, press on STAT select CALC, and then select Linreg(a + bx) . Next, we need to finish the command by entering L1L2

Linreg(a + bx)L1L2

Finally, pressing on ENTER then gives us the following result:

y = a + bx

a = 11.3891

b = 0.0308

r = 0.1

This then implies the regression line as:

Y= a + bx

鈬扽 = 11.3891 + 0.0308x

For the case without outlier:

Using a calculator, press on STAT and then select 1 : Edit. and then enter the data of sugar in the list L1 and enter the data of calories in the list L2

Next, press on STAT select CALC, and then select Linreg(a + bx) . Next, we need to finish the command by entering L1L2

Linreg(a + bx)L1L2

Finally, pressing on ENTER then gives us the following result:

y = a + bx

a = 14.0336

b = 0.0076

r = 0.0180

This then implies the regression line as:

Y= a + bx

鈬扽 = 14.0336 + 0.0076x

Thus, we note that the correlation coefficient with the outlier is more than the correlation coefficient without the outlier. We then note that the outlier increases the correlation due to the fact that game 16 as the correlation is much higher. When the outlier is removed the regression line becomes much more horizontal and thus game 16 makes the regression line less horizontal.

04

Part (c) Step 1: Explanation

For the case with outlier:

Using calculator, press on STAT and then select 1 : Edit . and then enter the data of sugar in the list L1 and enter the data of calories in the list L2

Next, press on STAT select CALC and then select Linreg(a + bx) . Next we need to finish thecommand by entering L1L2

Linreg(a + bx)L1L2

Finally, pressing on ENTER then gives us the following result:

y = a + bx

a = 11.3891

b = 0.0308

r = 0.1

This then implies the regression line as:

Y= a + bx

鈬 Y= 11.3891 + 0.0308x

For the case without outlier:

Using calculator, press on STAT and then select 1: Edit . and then enter the data of sugar in the list L1 and enter the data of calories in the list L2

Next, press on STAT select CALC and then select Linreg(a + bx) . Next we need to finish thecommand by entering L1L2

Linreg(a + bx)L1L2

Finally, pressing on ENTER then gives us the following result:

y = a + bx

a = 7.2776

b = 0.0505

r = 0.3182

This then implies the regression line as:

Y= a + bx

鈬扽 = 7.2776 + 0.0505x

Thus, we note that the correlation coeff icient with the outlier is more than the correlationcoeff icient without outlier. Then the game 13 makes the correlation decrease as the correlationcoeff icient is much lower. When the outlier is removed the regression line becomes much steeperand thus the game 13 makes the regression line steep.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Do muscles burn energy? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. We have data on the lean body mass and resting metabolic rate of 12 women who are subjects in a study on dieting. Lean body mass, given in kilograms, is a person鈥檚 weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours. The researchers believe that lean body mass is an

important influence on metabolic rate.

a. Make a scatterplot to display the relationship between lean body mass and metabolic rate.

b. Describe the relationship between lean body mass and metabolic rate.

One child in the Mumbai study had height 59 cm and arm span 60 cm. This child鈥檚 residual is

a. 鈭3.2 cm.

b. 鈭2.2 cm.

c. 鈭1.3 cm.

d. 3.2 cm.

e. 62.2 cm.

The scatterplot shows the lean body mass and metabolic rate for a sample of = adults. For each person, the lean body mass is the subject鈥檚 total weight in kilograms less any weight due to fat. The metabolic rate is the number of calories burned in a 24-hour period.

Because a person with no lean body mass should burn no calories, it makes sense to model the relationship with a direct variation function in the form y = kx. Models were tried using different values of k (k = 25, k = 26, etc.) and the sum of squared residuals (SSR) was calculated for each value of k. Here is a scatterplot showing the relationship between SSR and k:

According to the scatterplot, what is the ideal value of k to use for predicting metabolic rate?

a. 24

b. 25

c. 29

d. 31

e. 36

Correlation isn鈥檛 everything Marc and Rob are both high school English teachers. Students think that Rob is a harder grader, so Rob and Marc decide to grade the same 10 essays and see how their scores compare. The correlation is r=0.98 but Rob鈥檚 scores are always lower than Marc鈥檚. Draw a possible scatterplot that illustrates this situation.

Will I bomb the final? We expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary Smith of Pomona College looked at the exam scores of all 346 students who took his statistics class over a 10-year period. 17 The least-squares line for predicting final-exam score from midterm-exam score was y=46.6+0.41x . Octavio scores 10 points above the class mean on the midterm. How many points above the class mean do you predict that he will score on the final? (This is an example of the phenomenon that gave 鈥渞egression鈥 its name: students who do well on the midterm will on the average do less well, but still above average, on the final.)

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.