Consider the data. xi 2 6 9 13 20 yi 9 18 9 25 23 The estimated regression equation for these data is ŷ = 8.8 + 0.8x. What percentage of the total sum of squares can be accounted for by the estimated regression equation? (Round your answer to one decimal place.) % What is the value of the sample correlation coefficient? (Round your answer to three decimal

Consider the data. xi 2 6 9 13 20 yi 9 18 9 25 23 The estimated regression equation for these data is ŷ = 8.8 + 0.8x. What percentage of the total sum of squares can be accounted for by the estimated regression equation? (Round your answer to one decimal place.) % What is the value of the sample correlation coefficient? (Round your answer to three decimal

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.6: Regression And Median-fit Lines

Problem 4PPS

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

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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.
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?
The Pearson correlation between X1 and Y is r = 0.40. When a second variable, X2, is added to the regression equation, we obtain R2 = 0.64. How much variance for the Y scores is predicted by using both X1 and X2 as predictor variables? 0.40 or 40% 0.64 or 64% 0.48 or 48% 0.16 or 16%
a.) Calculate the sample correlation coefficient r. Using technology, find the following (show your work by copying and pasting your output and by writing up your finding):b.) The multiple regression equation for the data shown in the table abovec.) The standard error of estimate.d.) The coefficient of determinatione.) What is the percentage of explained variation?f.) What is the percentage of unexplained variation?
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.
A professor obtains SAT scores and freshman grade point averages (GPA) for a group of n=15 college students. The SAT scores have a mean of M=580 with SS=22,400, and GPA has a mean of 3.10 with SS=1.26, and SP=84. a. Find the regression equation for predicting GPA from SAT scores. b. What percentage of the variance in GPA is accounted for by the regression equation? (Compute the correlation, r, then find r2.) c. Does the regression equation account for a significant portion of the variance in GPA? Use α=.05 to evaluate the F-ratio.
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n = 15 college students. The SAT scores have a mean of M = 580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation r, then find r^2.) Does the regression equation account for a significant portion of the variance in GPA? Use α = .05 to evaluate the F-ratio.
A professor obtains SAT scores and freshman grade point averages (GPAs) for a group of n=15 college students. The SAT scores have a mean of M=580 with SS = 22,400, and the GPAs have a mean of 3.10 with SS = 1.26, and SP = 84. Find the regression equation for predicting GPA from SAT scores. What percentage of the variance in GPAs is accounted for by the regression equation? (Compute the correlation, r, then find r2.) C) Does the regression equation account for a significant portion of the variance in GPA? Use alpha = 0.05 to evaluate the F-ratio. A) b=0.00375; a=0.925; Y (hat) = 0.00375X+0.925 B) r= 0.5 r^2= 0.25
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation? r=0.926