stion 4 of 14 >The scatterplot given compares data on the fuel consumption y of a car at various speeds x. Fuel consumption is measured inliters of gasoline per 100 kilometers driven, and speed is measured in kilometers per hour. A statistical software package givesthe least-squares regression line ŷ = 11.058 +0.01466x.10.0 -Use the residual plot to determine if this linear model is75appropriate.O No. There is an obvious positive- negative - positive5.0 -pattern in the residual plot so a linear model is notappropriate for these data.O Yes. There is an obvious positive – negative –positive pattern in the residual plot so-a linear modelis appropriate for these data:O No. The residuals do not have equal variability in theresidual plot so a linear model is not appropriate for2.5 --2.5-5.0 -20406080100120140160these data.Speed (km/h)O No. The residuals are not equally positive or negativein the residual plot so a linear model is notappropriate for these data.O Yes. The residuals have such small values that alinear model is appropriate for these data.Residual

Solution: The least square regression line is y^=11.058+0.01466x Residual plot: The residual plot…

Answered: The scatterplot given compares data on…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.CR: Review Exercises

Problem 90CR

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
A pediatrician wants to determine the relationship that exists between achild’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below: (a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?
The data regarding the production of wheat in tons (X) and the price of the kilo of flour in Ghana cedis (Y) Takoradi some years ago were: a. Fit the regression line for the day using the method of least squares
Draw a graph of the least-squares regression line on your scatterplot. (For hand-drawing, round the slope and y-intercept to one decimal place before drawing the line.) Be sure to show how you were able to plot the line starting with its equation. Model City Miles per Gallon Highway Miles per Gallon Acura RLX 20 29 BMW 530i 24 34 Buick LaCrosse eAssist 25 35 Chevrolet Malibu 29 36 Ford Hybrid FWD 43 41 Honda Civic 32 42 Infiniti Q50 Red Sport 20 26 Kia Forte 30 40 Lexus ES 350 22 33 Mercedes Benz AMG S 21 30 Mini Cooper Clubman 24 32 Nissan Maxima 20 30 Suburu Legacy AWD 25 34 Toyota Prius ECO 58 53
Suppose Tatiyana is interested in the relationship between language ability and time spent reading. She randomly selects a sample of 30 students from the local high school and collects their scores from a language aptitude test. She surveys the sample asking each student how many hours per month he or she spends reading. Using the sample data, Tatiyana produces a scatterplot with reading time on the horizontal axis and language test scores on the vertical axis. She develops a least squares regression equation where ? is the amount of time spent reading during the month and ?̂ is the predicted value of the language test score. ?̂=3.251x+31.237 Compute the value of ?̂ when a student spends 42 hours reading. Give your answer precise to one decimal place. Avoid rounding until the last step. ?̂= ? points Identify all of the true statements regarding the interpretation of ?̂ when ?=42. The value of ?̂ is ? a. the predicted number of students that read for 42 hours. b. the language test…
A set of paired data has a least squares regressionline with equation yn = 0.50x + 2.0 and a correlationcoefficient of r = 0.80. Suppose we convert the datafor each variable to z-scores and then compute the newregression line. What will the equation be?A) zˆy = 0.50zx B) zˆy = 0.64zxC) zˆy = 0.80zx D) zˆy = 0.50zx + 20E) zˆy = 0.80zx + 20
The following table shows the length, in centimeters, of the humerus and the total wingspan, in centimeters, of several pterosaurs, which are extinct flying reptiles. (A graphing calculator is recommended.) (a) Find the equation of the least-squares regression line for the data. (Where × is the independent variable.) Round constants to the nearest hundredth. y= ? (b) Use the equation from part (a) to determine, to the nearest centimeter, the projected wingspan of a pterosaur if its humerus is 52 centimeters. ? cm
Using the least-squares regression line, y=-25.5+1.5x, what is the residual for the data point at (28,19)?
An experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. ∑ X = 30 ∑ X 2 = 104 ∑ Y = 40 ∑ Y 2 = 178 ∑ XY = 134 Using the simple linear regression model, find the estimated y-intercept and slope and write the equation of the least squares regression line.
A financial analyst is examining the relationship between stock prices and earnings per share. She chooses publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be =y+−0.2130.046x. This line, along with a scatter plot of her data, is shown below. Based on the sample data and the regression line, complete the following. (a)For these data, current stock prices that are less than the mean of the current stock prices tend to be paired with values for earnings per share that are ▼(Choose one) the mean of the values for earnings per share. (b)According to the regression equation, for an increase of one dollar in earnings per share, there is a…
A magazine publishes restaurant ratings for various locations around the world. The magazine rates the restaurants for food, decor, service, and the cost per person. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the three ratings. The magazine has compiled the accompanying table of this summated ratings variable and the cost per person for 25 restaurants in a major city. Assuming a linear relationship, use the least-squares method to compute the regression coefficients b0 and b1.
Solve the following problems completely. An article in the Journal of Environmental Engineering (1989, Vol. 115(3), reported the results of a study on the occurrence of sodium and chloride in surface streams in central Rhode Island. The following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage). Draw a scatter diagram of the data. Fit the simple linear regression model using the method of least squares. Find an estimate of σ2. Estimate the mean chloride concentration for a watershed that has 1% roadway area. Find the fitted value corresponding to x = 0.47 and the associated residual. Test the hypothesis H0: β1 = 0 versus H1: β1 ≠ 0 using the analysis of variance procedure with α = 0.01. Find a 99% confidence interval of Mean chloride concentration when roadway area x = 1.0% Find a 99% prediction interval on chloride concentration when roadway area x = 1.0%. Plot the residuals versus ŷ and versus x. Interpret these plots.…

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