4. Can the speed of a vehicle be predicted by the age of its driver? The speeds Y (inkm/h) of a sample of ten vehicles are recorded, along with the ages X of their drivers.From the data, we calculate i = 48.2, j = 107.8, (z:-2)² = 3669.6, (4- û)° =752.7. The least squares regression line is calculated to be ŷ = 133.198 – 0.527x.It is also determined that 57.5% of the variation in the speed of a vehicle can beaccounted for by its regression on the age of the driver.(a) What is the value of the correlation between the age of a driver and the speedof a vehicle?(b) Provide an interpretation of the slope of the least squares regression line.(c) Calculate a 95% confidence interval for the parameter 31 in the simple linearregression model.(d) We would like to conduct a hypothesis test at the 5% level of significance todetermine whether a linear relationship exists between the age of a driver andthe speed of a vehicle. Could the confidence interval in (c) have been usedto conduct the test? Why or why not? If it could be used, what would theconclusion be, and why?

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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…
The least-square regression line for the given data is y = 0.449x - 30.27. Determine the residual of a data point for which x = 90 and y=10, rounding to three decimal places. Temperature, x Number of absences, y OA. -0.14 OB. 20.14 C. 115.78 OD. 10.14 72 3 85 7 91 10 90 10 88 8 98 15 75 100 4 15 80- 5
The following gives the number of accidents that occurred on Florida State Highway 101 during the last 4 months: Month Number of Accidents Jan 25 Feb 40 Mar 60 Apr 90 Using the least-squares regression method, the trend equation for forecasting is (round your responses to two decimal places): ŷ-0-0x Using least-squares regression, the forecast for the number of accidents that will occur in the month of May = accidents (enter your response as a whole number).
A certain drug is used to treat asthma. In a clinical trial of the drug, 26 of 276 treated subjects experienced headaches (based on data from the manufacturer). The accompanying calculator display shows results from a test of the claim that less than 9% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.05 significance level to complete parts (a) through (e) below. 1-PropZTest prop < 0.09 z = 0.243984084 p = 0.5963784267 p = 0.0942028986 n = 276 a. Is the test two-tailed, left-tailed, or right-tailed? Two-tailed test Right tailed test Left-tailed test b. What is the test statistic? (Round to two decimal places as needed.) c. What is the P-value? P-value = (Round to four decimal places as needed.) d. What is the null hypothesis, and what do you conclude about it? Identify the null hypothesis. O A. Ho: p= 0.09 Click to select your answer(s). ?
5. Write the equation of the least-squares regression line defining any variables used. Round coefficients to 4 decimal places .
11. For temperature (x) and number of ice cream cones sold per hour (y). (65, 8), (70, 10), (75, 11), (80,13), (85, 12), (90, 16). Interpret the coefficient of determination. Optional Answers: 1. 88.2% of the variability in the number of cones sold is explained by the least-squares regression model. 2. 93.9% of the variability in the number of cones sold is explained by the least-squares regression model. 3. 88.2% of the variability in the temperature is explained by the least-squares regression model. 4. 93.9% of the variability in the temperature is explained by the least-squares regression model.
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.
3. Wine Participant magazine has collected average price per bottle for the prestigious Chateau Le Thundebird bordeaux for different vintages (years). The data appears in the table below. year of bottling price a) draw the scatter diagram showing how wine price varies by vintage year b) use the most appropriate regression equation to determine the relationship between year of bottling (age) and price. c) what is the explanatory power (RSQ) of that equation d) determine the predicted price of a bottle of this wine for the 2017 vintage. 2009 36 2010 40 2011 51 2012 60 2013 68 2014 72 2015 70 2016 65 2018 51 2019 44 2020 39
Below are bivariate data O each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is ing birthrate and life expectancy information for y = 81.87 – 0.46x. Birthrate, x (number of births per 1000 pop.) Female life expectancy, y (in years) 85- 35.7 67.7 80- 41.5 63.9 75 31.9 63.3 19.9 73.0 70 50.5 60.4 65. 24.4 72.7 60- 50.1 63.2 55 13.8 72.5 50 50.3 54.6 45.6 57.9 15.9 76.2 Figure 1 26.6 71.9 Send data to Excel
A year-long fitness center study sought to determine if there is a relationship between the amount of muscle mass gained y(kilograms) and the weekly time spent working out under the guidance of a trainer x(minutes). The resulting least-squares regression line for the study is y=2.04 + 0.12x A) predictions using this equation will be fairly good since about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out. B)Predictions using this equation will be faily good since about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent working out C)Predictions using this equation will be fairly poor since only about 95% of the variation in muscle mass can be explained by the linear relationship with time spent working out D) Predictions using this equation will be fairly poor since only about 90.25% of the variation in muscle mass can be explained by the linear relationship with time spent…
Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both x, the number of births per one thousand people in the population, and y, the female life expectancy (in years), are given. Also shown are the scatter plot for the data and the least-squares regression line. The equation for this line is y = 81.87– 0.46x. Birthrate, x (number of births per 1000 рop.) Female life expectancy, y (in years) 85- 35.7 67.7 80 41.5 63.9 31.9 63.3 75+ メメ 19.9 73.0 70- 50.5 60.4 65- 24.4 72.7 60- 50.1 63.2 55 13.8 72.5 50 50.3 54.6 45.6 57.9 15.9 76.2 Figure 1 26.6 71.9

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