Consider the data. xi 2 6 9 13 20 yi 9 18 9 25 23 The estimated regression equation for these data is ŷ = 6.8 + 0.9x. (A) What percentage of the total sum of squares can be accounted for by the estimated regression equation? (Round your answer to one decimal place.) _____

Consider the data. xi 2 6 9 13 20 yi 9 18 9 25 23 The estimated regression equation for these data is ŷ = 6.8 + 0.9x. (A) What percentage of the total sum of squares can be accounted for by the estimated regression equation? (Round your answer to one decimal place.) _____

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter4: Exponential Functions

Section4.4: Modeling Nearly Exponential Data

Problem 4E: Special Rounding Instructions For this exercise set, round all regression parameters to three...

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x_i	2	6	9	13	20
y_i	9	18	9	25	23

Similar questions

XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict the stock price to be in January 2012? January 2013?
Noise and Intelligibility Audiologists study the intelligibility of spoken sentences under different noise levels. Intelligibility, the MRT score, is measured as the percent of a spoken sentence that the listener can decipher at a cesl4ain noise level in decibels (dB). The table shows the results of one such test. (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Find the correlation coefficient. Is a linear model appropriate? (d) Use the linear model in put (b) to estimate the intelligibility of a sentence at a 94-dB noise level.
Zipfs Law The following table shows U.S cities by rank in terms of population and population in thousands. City Rank r Population N New York 1 8491 Chicago 3 2722 Philadelphia 5 1560 Dallas 9 1280 Austin 11 913 San Francisco 13 852 Columbus 15 836 A rule known as Zipfs law tells us that it is reasonable to approximate these data with a power function. a Use power regression to express the population as a function of the rank. b Plot the data along with the power function from part a. c Phoenix is the sixth largest city in the United States. Use your answer from part a to estimate population of Phoenix. Round your answer in thousands to the nearest whole number. Note: The actual population is 1537 thousand.
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?
Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Postal RatesThe table below shows the cost s, in cents, of a domestic first-class postage stamp in the United States tyears after 1900. t=time,inyearssince1900 s=costofstamp 19 2 32 3 58 4 71 8 78 15 85 22 95 32 102 37 109 44 116 47 a.Use exponential regression to model s as an exponential function of t. b.What cost does your model give for a 1988 stamp? Report your answer to the nearest cent. The actual cost was 25cents. c.Plot the data and the exponential model.
Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Gray Wolves in WisconsinGray wolves were among the first mammals protected under the Endangered Species Act in the 1970s. Wolves recolonized in Wisconsin beginning in 1980.Their population grew reliably after 1985 as follows: Year Wolves Year Wolves 1985 15 1993 40 1986 16 1994 57 1987 18 1995 83 1988 28 1996 99 1989 31 1997 145 1990 34 1998 178 1991 40 1999 197 1992 45 2000 266 a. Explain why an exponential model may be appropriate. b. Are these data exactly exponential? Explain. c. Find an exponential model for these data. d. Plot the data and the exponential model. e. Comment on your graph in part d. Which data points are below or above the number predicted by the exponential model?
3.4 SKILL BUILDING EXERCISES Using the Regression Line In Exercises S-1 through S-4, you are asked to provide information using the given regression line. Utility Bill The regression line for a data set showing the monthly utility bill U in a certain city versus the square footage F of the residence is given by U=0.2F-100 dollars. What monthly utility bill would be expected for a 25400-square-foot home in this city?
Remainder Round all answers to two decimal places unless otherwise indicated. Gross Domestic Product U.S. gross domestic product, in trillions of dollars, is given in the table below. Date Gross domestic product 2010 15.0 2011 15.5 2012 16.2 2013 16.7 a.Find the equation of the regression line, and explain the meaning of its slope. Round regression line parameters to two decimal places. b.Plot the data points and the regression line. c.When would you predict that a gross domestic product of 17.3 trillion dollars would be reached? The actual gross domestic product in 2014 was 17.3 trillion dollars. What does that say about your prediction?
1. What is the greatest concern about the regression below? a) It has a small slope. b) It has a high . c) The investigator should not be using a linear regression on these data. d) The residuals are too large. e) The regression line does not pass through the origin. 2. The scatterplots below display three bivariate data sets. The correlation coefficients for these data sets are 0.03, 0.68, and 0.89. Which scatter plot corresponds to the data set with = 0.03? a) Plot 1 b) Plot 2 c) Plot 3
Solvent cement is used to join PVC joints. Researchers are interested in predicting the amount of time is needed for the joint to set (measured in hours) as it is related to temperature measured in degrees F for 4 to 8-inch diameter pieces. A random sample of PVC joints was taken and a linear regression model was found. Use the following output and the fact that R2 = 0.965 to answer the following questions. 4. Find the Correlation and interpret in the words of the problem. 5. Find the residual for a temperature of 60 F, if the time to set was 5.6 hours. 6. Find the residual for a temperature of 50 F, if the time to set was 5.4 hours.
Using the regression line attached. In the above plot, a rejection of the null hypothesis that the population regression slope is equal to 0 implies: a) the correlation coefficient in the population is likely equal to 0 b) the correlation coefficient in the population is likely unequal to 0 c) the standard deviation of height is likely very large d) the standard deviation of weight is likely very small e) the correlation coefficient must be close to 1.0 f) a and c g) b and e h) b, d and e
a) Determine the correlation coefficient, r, and interpret this value in the context of the problem. (Round 4 decimal places)b) Find the equation of the regression line for the given data. (Round the slope and y-intercept 4 decimal places).c) Give a practical interpretation of the slope of the regression line.