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

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 5PPS

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The graph shows a bivariate data set and its least squares regression line.
3.6
3.2
2.8
2.4
2
1.6+
1.2-
0.8
0.4-
←
2
4
Create (graph) a residual plot for the same data set.
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10
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Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. 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 as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300
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?
What is regression analysis? Describe the process of performing regression analysis on a graphing utility.
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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.
The graph shows a bivariate data set and its least squares regression line. Draw the residual plot for the same data set?
The least-squares regression equation is y = 753.6x + 12,900 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 55000- linear relation between the two variables with a correlation coefficient of 0.8274. Complete parts (a) through (d). 20000+ 15 20 25 30 35 40 45 50 55 60 Bachelor's % (a) 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.) (b) In a particular region, 28.8 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $37,925. Is this income higher than what you would expect? Why? This is than expected because the expected income is $ (Round to the nearest dollar as needed.) (c) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal. Do not…
please give handwritten
Regression analysis was applied and the least squares regression line was found to be ŷ = 300 + 4x. What would the residual be for an observed value of (3, 309)? -3 3 309 312
Draw a graph of the least-squares regression line on your scatterplot. (For hand-drawing, round the slope and y-intercept to one decimal place before drawing the line.) Be sure to show how you were able to plot the line starting with its equation. Model City Miles per Gallon Highway Miles per Gallon Acura RLX 20 29 BMW 530i 24 34 Buick LaCrosse eAssist 25 35 Chevrolet Malibu 29 36 Ford Hybrid FWD 43 41 Honda Civic 32 42 Infiniti Q50 Red Sport 20 26 Kia Forte 30 40 Lexus ES 350 22 33 Mercedes Benz AMG S 21 30 Mini Cooper Clubman 24 32 Nissan Maxima 20 30 Suburu Legacy AWD 25 34 Toyota Prius ECO 58 53
Looking at this output in the photo, we know that the proportion of the variation in mileage is accounted for by the linear relationship with the weight of the car is 43.8 % and that the estimate of the regression standard deviationis is 6.78. Determine the equation of the Least Squares Regression Line and what the interpretation of the slope for weight of car is? Then performing a T-test, determine what the value of the t stastitic is if we wanted to test if there is a significant straight-line relationship between the weight and the mileage of a car.
Interpret the slope of the least square regression line in content

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