1-8 The table shows the world populations y (in billions) for five different years. Let x = 8 represent the year 1998.†Year, x19982000 20026.1 6.220046.4Population, y 5.9(a) Use the regression capabilities of a graphing utility to find the least squares regression line for the data. (Round your answer to three decimal places.)y =(b) Use the regression capabilities of a graphing utility to find the least squares regression quadratic for the data. (Round your answer to three decimal places.)y =(c) Use a graphing utility to plot the data and graph the models.y0504201020066.51520XX20Oyy7.026.5k f6.010150101505.55.0y4+250 of1015How do the two models differ as you extrapolate into the future?O The linear model is less accurate.O The quadratic model is less accurate.0(d) Use both models to forecast the world population for the year 2014. (Round your answers to one decimal place.)linearbillionquadraticbillion2020XX

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Answered: The table shows the world populations y…

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 34EQ

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If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
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?
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be ŷ = 85 + 16x. The software used to compute the least-squares regression line for the equation above says that r2 = 0.98. This suggests which of the following? 1. Gas used increases by square root of 0.98 = 0.99 cubic feet for each additional degree-day? 2. Although degree-days and gas used are correlated, degree-days do not predict gas used very accurately. 3. Prediction of gas used from degree-days will be quite accurate.
The least-squares regression equation is y=728.0x+14,705 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.8165. For every dollar increase in median income, the percent of adults having at least a bachelor's degree is ___%, on average. For a median income of $0, the percent of adults with a bachelor's degree is ____%.
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.
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
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 least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. Predict the median income of a region in which 30% of adults 25 years and older have at least a bachelor's degree.
The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y=−0.006x+42.541. A twelfth car weighs 3,425pounds and gets 12 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R2? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Car Weight_(pounds),_x Miles_per_Gallon,_y1 3767 212 3989 193 3534 204 3175 225 2581 276 3736 207 2606…
(a) Find the equation of the least-squares line for the data. (Round all numerical values to two decimal places.) y= ?
Carbon dioxide (CO,) is produced by burning fossil fuels such as oll and natural gas, and has been connected to global warming. The following table presents the average amounts (in metric tons) of COy emissions for certain years per person in the United States and per person in the rest of the world. Use a TI-84 calculator to answer the following, (a) Compute the least-squares regression line for predicting U.S. emissions from non-U.S. emissions. Round the slope and y-intercept values to four decimal places.
A study was conducted to assess the relationship between students’s score in final exam (y) and number of hours spent for exam (x) in each day. Data on a random sample 20 students were obtained and a regression model was estimated; and the least squares estimates obtained are: intercept a=28.5 and slope b=4.3 with SE(b)=Sb=0.017. The SS are: TSS=2540 and ESS=850. ****** QA) What is the difference between exam score obtained by two students one who studied 5 hours and the other who studied 9 hours per day. QB) In the above Question 1, find 95% CI for the slope and interpret it. In the above Question 1, find and interpret the coefficient of determination (r-square value).

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