The total amount of construction spending on highways and streets (in billions of dollars) is given in the accompanying table for the first six months of 2016.January96February95March94April92June86MonthSpendingMay87(a) Find the least-squares regression line that models these data, with x = 1 corresponding to January 2016.(b) Assuming the trend continues, estimate the amount of spending in November 2016.(a) The linear model for the data is y = (x+ .(Round to the nearest thousandth as needed.)

The total amount of construction spending on highways and streets (in billion of dollars) is given…

Answered: The total amount of construction…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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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?
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
What is the slope of the least-squares regression line for these data? Carry your intermediate computations to at least four decimal places and round your answer to at least three decimal places.
Compute the least-squares regression line for predicting the 2012 budget from the 2006 budget. Round the slope and y. intercept to at least four decimal places.
At Hard Rock’s Moscow restaurant, the manager is trying to evaluate how a new advertising campaign affects guest counts. Using data for the past 10 months (see the table), develop a least-squares regression relationship and then forecast the expected guest count when advertising is $65,000.
The calories and sugar content per serving size of ten brands of breakfast cereal are fitted with a least squares regression line with computer outputs: (see picture) 1. What are the predicted calories for a brand with 10 g sugar per serving? 2. What were the actual calories for the brand with 10 g sugar per serving?
Is CEO compensation related to a company's performance? To test whether CEO compensation and a company's stock performance are related, a financial analyst collected data on 12 randomly selected, publicly traded companies. For each company, the analyst looked at two variables: the percent change in stock price over the past five years (which she denoted x ) and the percent change in CEO compensation over the past five years (which she denoted y ). For these 12 companies, the least-squares regression equation relating the two variables was =y+−0.1650.046x , and the standard error of the slope of this least-squares regression line was approximately 0.028 . Using her information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope β1 . (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the…
An engineer wants to determine how the weight of a gas-powered car, x, affects the gas mileage, y. Would it be reasonable to use the least-squares regression line to predict the miles per gallon of a hybrid gas and electric car? Why and why not?
A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. Assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1. Interpret the meaning of the slope, b1, in this problem. Predict the mean opening weekend box office gross for a movie that had 80 million online trailer views. What insights can be obtained about predicting opening weekend box office gross from online trailer views?
The following table presents the percentage of students who tested proficient in reading and the percentage who tested proficient in math for 5 randomly selected states in the United States. Compute the least-squares regression line for predicting math proficiency from reading proficiency. State Percent Proficientin Reading Percent Proficientin Mathematics Illinois 75 70 North Carolina 71 73 California 60 59 Georgia 67 64 Florida 66 68 Send data to Excel The equation for the least squares regression line is y = . Round the slope and y -intercept to four decimal places as needed.
A manager wishes to determine the relationship between the number of years her sales representatives have been employed by the firm and their amount of sales (in thousands of dollars) per month. Find the least-squares regression line for the given data. What would be the predicted sales if the sales representative was employed by the firm for 30 years? Is this reasonable? Why or why not? Round the least-squares regression line values to two decimal places. Years employed, x 2 3 10 7 8 15 3 1 11 Sales, y 31 33 78 62 65 61 48 55 120
find the least squares regression line equation from the given data.

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