An article in the Journal of Sound and Vibration (Vol. 151, 1991, pp. 383-394) described a study investigating the relationship betweennoise exposure and hypertension. The following data are representative of those reported in the article.y xyx1 60 5 850 63 4 89165 6 90270 8 905 70 4 901 70 5 904 80 7 946 90 9 100280 7 1003 80 6 100Fit a linear regression model relating blood pressure rise in millimeters of mercury (y) to sound pressure level in decibels (x) using leastsquares.(a) Draw a scatter diagram of y versus x (using statistical software). Does a simple linear regression model seem reasonable in thissituation?(b) Calculatnoyessquares estimate of the slope. ₁ =(Round your answer to 3 decimali(c) Calculate the least squares estimate of the intercept. Po =places.)(d) Calculate an estimate of o².(Round your answer to 3 decimal places.)(e) Obtain the predicted mean rise in blood pressure level associated with a sound pressure of 87 decibels.Άγιο1(Round your answer to 3 decimal places.)(Round your answer to 3 decimal An article in the Journal of Sound and Vibration (Vol. 151, 1991, pp. 383-394) described a study investigating the relationship betweennoise exposure and hypertension. The following data are representative of those reported in the article.y xy x1 60 5 850 63 4 891 65 6 90270 8 905 70 4 901 70 5 904 80 7 946 90 9 1002 80 7 1003 80 6 100Fit a linear regression model relating blood pressure rise in millimeters of mercury (y) to sound pressure level in decibels (x) using leastsquares.(a) Draw a scatter diagram of y versus x (using statistical software). Does a simple linear regression model seem reasonable in thissituation?(b) Calculate the least squares estimate of the slope. /₁ = 1(Round your answer to 3 decimal places.)(c) Calculate the least squares estimate of the intercept. B =places.)(Round your answer to 3 decimal(d) Calculate an estimate of o².i(Round your answer to 3 decimal places.)(e) Obtain the predicted mean rise in blood pressure level associated with a sound pressure of 87 decibels.YTO(Round your answer to 3 decimal places.)

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Answered: An article in the Journal of Sound and…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.CR: Review Exercises

Problem 90CR

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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?
The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
The following table shows data for the cost of natural gas in Maryland (in dollars per Million Btu) for x years since 1990. Year x Price in $ per Million Btu 1990 6.31 1991 6.14 1992 6.32 1993 6.75 1994 6.8 1995 6.34 1996 7.46 1997 8.12 1998 8.04 1999 8.25 2000 9.58 2001 11.28 2002 9.25 a. Define the explanatory and response variables for this problem. b. Use the calculator to obtain the linear regression line of best fit for the original prices; round to three decimal places. Write this prediction equation in the form: a. In a brief sentence, interpret the slope in the context of the problem.
The monthly premium quoted by an insurance company for a critical illness policy was collected from a sample of 6 adult male smokers at different age. The data for the sample are shown: Age 28 25 50 39 47 31 Premium ($) 75 40 175 125 250 105 Using Age to predict premium, the Linear Regression equation is given by: ŷ =6.556X−112 and r2=0.813y^=6.556X−112 and r2=0.813 a. Identify the independent and Dependent variables. Dependent: Age Premium Independent: Age Premium b. Determine the slope. Slope = Slope = Round to 3 decimal places c. Determine |r||r| . |r|=|r|= Round to 3 decimal places d. Interpret rr : and e. Determine critical r value at 5% significance level and determine if there is a significant linear correlation exists. |r| critical=|r| critical= Round to 3 decimal places Linear Correlation:Linear Correlation: Significant Not Significant f. Predict the monthly premium for a 40 years old adult male smoker.…
Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 220 2,640 144 48,400 10 15.5 190 2,945 240.25 36,100 Total 151 1,760 26,050 2,312 320,800 Regression Parameters Estimations Slope (ββ) -16.49 Intercept (αα) 424.98 In words, for a dollar increase in the selling price, the expected sales will increase by 2,640 gallons in a given sales region.…
Suppose the Sherwin-Williams Company is interested in developing a simple regression model with paint sales (Y) as the dependent variable and selling price (P) as the independent variable. Complete the following worksheet and then use it to determine the estimated regression line. Sales Region Selling Price Sales ($/Gallon) (x 1000 Gal) ii xixi yiyi xixiyiyi xi2xi2 yi2yi2 1 15 160 2,400 225 25,600 2 13.5 220 2,970 182.25 48,400 3 16.5 140 2,310 272.25 19,600 4 14.5 190 2,755 210.25 36,100 5 17 120 2,040 289 14,400 6 16 160 2,560 256 25,600 7 13 210 2,730 169 44,100 8 18 150 2,700 324 22,500 9 12 210 2,520 144 44,100 10 15.5 190 2,945 240.25 36,100 Total 151 1,750 2,312 What is the estimate of the standard deviation of the estimated slope (sbsb)? 2.627 3.173 2.877 Can you reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., β=0β=0) between the…
The following table displays the EPA fuel efficiency estimates (in miles per gallon) and the curbweight (in pounds) for a random sample of current year model vehicles.MPG 23 18 28 19 25 17 18 14Weight 3184 3598 2734 4082 2623 4685 4178 5488(a) Determine the linear regression model that will best predict the EPA fuel efficiency estimates(MPG) of a vehicle based on its curb weight.(b) How well does the linear regression model fit this sample data?(c) For a vehicle that weighs 4000 pounds, predict its EPA fuel efficiency estimate.
A random sample of twelve students were chosen, and their midterm test score (y), as- signment score (x1), and missed classes (x2) were recorded as follows: Midterm Score, y Assignment Score, x1 Classes Missed, x2 85 74 76 90 85 87 94 98 81 91 76 74 65 50 55 65 55 70 65 70 55 70 50 55 5 7 5 2 6 3 2 5 4 3 1 4 (i) What is the fitted multiple linear regression equation of the form yˆ = b0 + b1x1 + b2x2? (ii) From part (i) above, estimate the midterm test score grade for a student who has an assignment score of 60 and missed 4 classes.
The authors of a paper were interested in how the distance a deer mouse will travel for food is related to the distance from the food to the nearest pile of debris. Distances were measured in meters. The data and computer output are given below. Distance from Debris Distance Traveled 6.94 0.00 5.23 6.13 5.21 11.29 7.10 14.35 8.16 12.03 5.50 22.72 9.19 20.11 9.05 26.16 9.36 30.65 Simple Linear Regression Results: Dependent Variable: Traveled Independent Variable: Debris Sample size: 9 R (correlation coefficient) = 0.5657 R-sq = 0.32002088 Estimate of error standard deviation 8.670711 Parameter estimates: Parameter Estimate Std. Err. Alternative DF T-Stat P-Value Intercept -7.6854587 13.332196 ≠ 0 7 -0.5764586 0.5824 Slope 3.2340908 1.7818117 ≠ 0 7 1.8150575 0.1124 a)What is the least squares regression line for the output given above? b) what is the predicted traveled distance given the distance from debris is 6.5 meters?
King & Scott, a research firm for the real estate industry, studied the relation between x=x= annual income (in thousands of dollars) and y=y= sale price of house purchased (in thousands of dollars). A random sample of data was collected from mortgage applications for home sales in the region of the study, and is given in the table. Annual Income House Price 72 188 48 91.6 73 182.2 97 155.5 97 238.8 94 203.4 67 160.1 85 212 64 169 Conduct a linear regression. Use the results to answer the following questions. a. What is the value of the correlation coefficient (round to 3 decimal places)? What does the value tell you about the linear relationship between the annual income and the price of house purchased? Correlation coefficient: This indicates: very weak positive linear correlation fairly strong negative linear correlation perfect positive linear correlation very weak negative linear correlation perfect negative linear correlation no linear…
Suppose a study wants to predict the market price of a certain species of turtle (Y) based on the following independent variables indicated in the table. Based from the table, what is the equation of the multiple linear regression? (Round off up to two decimal places. Market Price = 0.07 - 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = - 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = 0.07 + 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = 0.07 - 0.40 + weight + 1.51 + length + 1.41 + width + 0.80 + age

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