Mass-Transit Subsidies The following table gives the projected state subsidies (in millions of dollars) to a certain transit authority over a 5-year period (x = 1 corresponds to the first year). Year, x 1 2 3 4 5 Subsidy, y 21.25 25.5 24.25 26.25 33.75 (a) Find an equation of the least-squares line for these data. (b) Assuming that the trend continued, estimate the state subsidy to the MBTA (in millions of dollars) for the eighth year (x = 8). (Round your answer to one decimal place.) million

Mass-Transit Subsidies The following table gives the projected state subsidies (in millions of dollars) to a certain transit authority over a 5-year period (x = 1 corresponds to the first year). Year, x 1 2 3 4 5 Subsidy, y 21.25 25.5 24.25 26.25 33.75 (a) Find an equation of the least-squares line for these data. (b) Assuming that the trend continued, estimate the state subsidy to the MBTA (in millions of dollars) for the eighth year (x = 8). (Round your answer to one decimal place.) million

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

See similar textbooks

Similar questions

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?
Draw a scatterplot of the right foot temperature (y) versus the left foot temperature (x). Then draw the least-squares regression line on the graph.
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 ____%.
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.
The least-squares regression equation is y=784.6x+12,431 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 0.7962. Predict the median income of a region in which 25% of adults 25 years and older have at least a bachelor's degree.
The least-squares regression equation is y=784.6x+12,431 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 0.7962. In a particular region, 26.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $29,889. Is this income higher or lower than what you would expect? Why?
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. In a particular region, 28.3 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $37,389. Is this income higher than what you would expect? Why?
The least-squares regression equation is y=647.8x+17,858 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 0.7507. predict the median income of a region in which 20% of adults 25 years and older have at least a bachelor's degree. Round to the nearest dollar as needed.
(a) Find the equation of the least-squares line for the data. (Round all numerical values to two decimal places.) y= ?
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?
1) Calculate the slope b1 and intercept b0 of the least squares prediction line y = b0 + b1x where the x-variable is time spent on Facebook and the y-variable is GPA. a) slope b) intercept 2) what is the predicted GPA of a student that spends 60 minutes a day on Facebook?
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.