48. See photo A study was conducted to compare the average time spent in the lab each week versus course grade forcomputer students. The results are recorded in the table below.O A. Extremely usefulO B. Moderately usefulHours spentGradein lab(percent)O C. Not very useful1096O D. Not enough information115116629.58789158116461051State how useful the regression equation appears to be for making predictions.

Solution Regression equation is useful if correlation coefficient is high,here the correlation…

Answered: A study was conducted to compare the…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 6SGR

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
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 does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
Cellular Phone Subscribers The table shows the numbers of cellular phone subscribers y in millions in the United States from 2008 through 2013. Source: CTIA- The Wireless Association Year200820092010201120122013Number,y270286296316326336 (a) Find the least squares regression line for the data. Let x represent the year, with x=8 corresponding to 2008. (b) Use the linear regression capabilities of a graphing utility to find a linear model for the data. How does this model compare with the model obtained in part a? (c) Use the linear model to create a table of estimated values for y. Compare the estimated values with the actual data.
For the following exercises, use Table 4 which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year. Based on the set of data given in Table 5, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy
Researchers are investigating how the amount of monthly rainfall, measured in centimeters (cm), affects the monthly growth, in cm, of a certain plant. From a sample of data, the researchers created a least- squares regression line. Computer output is shown in the following table. Variable DF Estimate SE T Intercept 1 0.75 0.350 2.14 Rainfall 1 0.15 0.025 6.00 Which of the following statements is an interpretation of the value 0.75 shown in the table? A Monthly growth is expected to increase by 0.75 cm when rainfall increases by 1 cm. Rainfall is expected to increase by 0.75 cm when monthly growth increases by 1 cm. For a month with 0 cm of rainfall, the monthly growth is expected to be approximately 0.75 cm. For a plant with 0 cm of monthly growth, the month had an expected rainfall of approximately 0.75 cm. E Approximately 75% of the variability in monthly growth is due to its linear relationship with rainfall.
In a particular manufacturing process, the useful life of a cutting tool is linearly related to the speed at which the tool is operated. The data in the accompanying table were derived from life tests for the two different brands of cutting tools currently used in the production process. For which brand would you feel more confident using the least squares line to predict useful life for a given cutting speed? E Click the icon to view the data. Since the standard deviation (s = for Brand B is than the standard deviation for Brand A (s = ), Brand B would be a predictor for the useful life for a given cutting speed. (Type an integer or a decimal rounded to three decimal places.) - X Data Table Useful Life (hours) Cutting Speed (meters per minute) Brand A Brand B 30.0 4.7 6.0 30.0 3.5 6.5 30.0 5.4 5.0 40.0 5.4 6.0 40.0 4.0 4.5 40.0 2.5 5.0 50.0 4.4 4.5 50.0 2.8 4.0 50.0 1.0 3.6 60.0 4.0 3.7 60.0 2.0 3.0 60.0 1.1 2.4 70.0 1.5 1.5 70.0 0.5 2.0 70.0 4.0 1.0
Researchers are investigating how the amount of monthly rainfall, measured in centimeters (cm), affects the monthly growth, in cm, of a certain plant. From a sample of data, the researchers created a least-squares regression line. Computer output is shown in the following table. Which of the following statements is an interpretation of the value 0.75 shown in the table?
A highway employee performed a regression analysis of the relationship between the number of construction work-zone fatalities and the number of unemployed people in a state. The regression equation is Fatalities = 12.7 + 0.000114 (Unemp). Some additional output is: Predictor Coef SE Coef T P Constant 12.726 8.115 1.57 0.134 Unemp 0.00011386 0.00002896 3.93 0.001 Analysis of Variance Source DF SS MS F P Regression 1 10,354 10,354 15.46 0.001 Residual Error 18 12,054 670 Total 19 22,408 a. How many states were in the sample? b. Determine the standard error of estimate. (Round your answer to 2 decimal places.) c. Determine the coefficient of determination. (Round your answer to 2 decimal places.) d. Determine the correlation coefficient. (Round your answer to 2 decimal places.)
The following data represent the time between eruptions and the length of eruption for 8 randomly selected geyser eruptions. The coefficient of determination is 87.6%. Provide an interpretation of this value. Click here to view a scatter plot of the data. Click here to view a residual plot of the data. The coefficient of determination is found to be 87.6%. Provide an interpretation of this value. The least squares regression line explains % of the variation in (Type an integer or decimal. Do not round.) Time, x 12.16 11.77 12.04 12.13 11.31 Length, y 1.87 1.81 1.83 1.83 1.63 Time, x 11.74 12.25 11.64 11.69 Length, y 1.70 1.88 1.71 1.77
A researcher records data on 7 adult pairs' heights (in inches) to compare the physical characteristics of brothers and sisters. Brother Sister 71 69 68 64 6 65 67 63 70 65 71 62 66 62 Mean 68.4285 64.2857 SD 2.2253 2.4299 r=0.4050 What would the least-squares regression equation be for predicting the brother's height from the sister's? A. brother's height = 0.037+44.58 * sister's height B. brother's height = 44.58 + 0.371* sister's height C. brother's height = 20.71 + 0.029 * sister's height D. brother's height = 3.28- 40.68 * sister's height If the sister's height is the same as the mean (64.2857 inches), what would the brother's predicted height be A. 68.4285 (the same as the mean as well) B. 62.1234 C. 70.8990 D. None of the above. Which of the following would be correct? A. The pair of means, (68.4285, 64.2857), lies on the linear regression line. B. The effectiveness of the linear regression model is about 16%, C. The effectiveness of the linear regression model is 10096. D. Both…

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