/*! 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 61. Temperature and wind The average... [FREE SOLUTION] | 91影视

91影视

Temperature and wind The average temperature (in degrees Fahrenheit) and average wind speed (in miles per hour) were recorded for 365 consecutive days at Chicago鈥檚 O鈥橦are International Airport. Here is the computer output for regression of y = average wind speed on x = average temperature:

a. Calculate and interpret the residual for the day where the average temperature was 42掳F and the average wind speed was 2.2 mph.

b. Interpret the slope.

c. By how much do the actual average wind speeds typically vary from the values predicted by the least-squares regression line with x = average temperature?

d. What percent of the variability in average wind speed is accounted for by the least-squares regression line with x = average temperature?

Short Answer

Expert verified

Part (a) Residual is 7.972528

Part (b) The average wind speed reduces by 0.041077miles per hour per degree Fahrenheit.

Part (c) The average deviation between the anticipated average wind speed and the actual average wind speed was 3.655950mph using the equation of the least square regression line.

Part (d) The least square regression line using average temperature as an explanatory variable explains 4.7874 percent of the variation in average wind speed.

Step by step solution

01

Part (a) Step 1: Given information

The relationship of average temperature and the average wind speed in given in the question.

02

Part (a) Step 2: Concept

The formula used:Residual=yy

03

Part (a) Step 3: Calculation

The general equation of the least square regression line is:

y=b0+b1x

As a result, the estimate of the constant b0 is given in the computer output's row "Intercept" and column "Estimate" as:

b0=11.897762

In the computer output, the estimate of the slope b1 is given in the row "Avg temp" and the column "Estimate" as:

b1=0.041077

As a result, when we plug the values into the general equation, we get:

y=b0+b1xy=11.8977620.041077x

As a result, the average wind speed at 42degrees Fahrenheit is:

y=11.8977620.041077x=11.8977620.041077(42)=10.172528

Thus the residual will be calculated as:.

Residual=yy=2.210.172528=7.972528

This means that while using the regression line to make a prediction, we underestimated the average wind speed on the day with an average temperature of 40Fby7.972528 mph.

04

Part (b) Step 1: Calculation

The question specifies the link between average temperature and average wind speed. The regression line is as follows:

y=11.8977620.041077x

The slope is the coefficient of x in the least-squares regression equation, and it reflects the average rise or decrease of y per unit of x as we all know. Thus,

b0=10.041077

As a result, the average wind speed reduces by0.041077 miles per hour per degree Fahrenheit.

05

Part (c) Step 1: Calculation

The question specifies the link between average temperature and average wind speed. The regression line is as follows:

y=11.8977620.041077x

The standard error of the estimate s is calculated as follows in the computer output following "root mean square error":

s=3.655950

The standard error of the estimations, as we all know, is the average error of forecasts, and thus the average difference between actual and predicted values. As a result, using the equation of the least square regression line, the predicted average wind speed differed by 3.655950 mph on average from the actual average wind speed.

06

Part (d) Step 1: Explanation

The question specifies the link between average temperature and average wind speed. The regression line is as follows:

y=11.8977620.041077x

The coefficient of determination is given as follows in the computer output after "RSquare":

r2=0.0478742=4.7874%

The coefficient of determination, as we all know, represents the proportion of variance in the answers y variable that can be explained by a least square regression model using the explanatory x variable. As a result, we can state that the least square regression line employing average temperature as an explanatory variable explains 4.7874 percent of the variation in average wind speed.

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

More Olympic athletes In Exercises 5 and 11, you described the relationship between height (in inches) and weight (in pounds) for Olympic track and field athletes. The scatterplot shows this relationship, along with two regression lines. The regression line for the shotput, hammer throw, and discus throw athletes (blue squares) is y^=鈭115+5.13x. The regression line for the remaining athletes (black dots) is y^=鈭297+6.41x

a. How do the regression lines compare?

b. How much more do you expect a 72-inch discus thrower to weigh than a 72-inch sprinter?

Crickets chirping The scatterplot shows the relationship between x = temperature in degrees Fahrenheit and y = chirps per minute for the striped ground cricket, along with the regression line y^=鈭0.31+0.212x

a. Calculate and interpret the residual for the cricket who chirped 20 times per minute when the temperature was 88.6掳F.

b. About how many additional chirps per minute do you expect cricket to make if the temperature increases by 10掳F?

Teaching and research A college newspaper interviews a psychologist about student ratings of the teaching of faculty members. The psychologist says, 鈥淭he evidence indicates that the correlation between the research productivity and teaching rating of faculty members is close to zero.鈥 The paper reports this as 鈥淧rofessor McDaniel said that good researchers tend to be poor teachers, and vice versa.鈥 Explain why the paper鈥檚 report is wrong. Write a statement in plain language (don鈥檛 use the word correlation) to explain the psychologist鈥檚 meaning.

Fuel economy (2.2) In its recent Fuel Economy Guide, the Environmental Protection Agency (EPA) gives data on 1152 vehicles. There are a number of outliers, main vehicles with very poor gas mileage or hybrids with very good gas mileage. If we ignore the outliers, however, the combined city and highway gas mileage of the other 1120 or so vehicles is approximately Normal with a mean of 18.7 miles per gallon (mpg) and a standard deviation of 4.3 mpg.

a. The Chevrolet Malibu with a four-cylinder engine has a combined gas mileage of 25 mpg. What percent of the 1120 vehicles have worse gas mileage than the Malibu?

b. How high must a vehicle鈥檚 gas mileage be in order to fall in the top 10% of the 1120 vehicles?

Scientists examined the activity level of 7 fish at different temperatures. Fish activity was rated on a scale of 0 (no activity) to 100 (maximal activity). The temperature was measured in degrees Celsius. A computer regression printout and a residual plot are provided. Notice that the horizontal axis on the residual plot is labeled 鈥淔itted value,鈥 which means the same thing as 鈥減redicted value.鈥

What is the correlation between temperature and fish activity?

a. 0.95

b. 0.91

c. 0.45

d. 鈥0.91

e. 鈥0.95

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.