Consider the following data and create a linear regression model: Data 1 2 3 6 Y 6 6 11 12 O y=1.7x+1.4 O y=2x+1 O y=1.4x+1.7
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- The table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a linear model that express Vitamin C content as a function of the weight of the Raspberries. use excel grams Vitamin Ccontent in mg 60 14.3 75 21 90 27 105 34.3 120 41 135 48.7 150 54 A) Find the regression equation: y = + xxRound your answers to 3 decimal places B) Answer the following questions using your un-rounded regression equation. If we test 180 grams of raspberries what is the expected Vitamin C content? mgmg (round to the nearest tenth)Suppose there is 1 dependent variable (dissolved oxygen, Y) and 3 independent variables (water temp X1, depth X2, and hardness of water X3). Below is the result of the multiple linear regression.Which of the following is the equation of the multiple regression model? Y = 4.36 + 0.37X1 + 0.24X2 + 0.04X3 Y = 0.00 + 0.02X1 + 0.56X2 + 0.37X3 Y = 24.84 - 1.17X1 - 0.15X2 - 0.04X3 Y = 5.69 – 3.20X1 - 0.61X2 -0.95X3The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. Below is the data that represents the value (in $millions) and the annual revenue (in $millions) for 30 Major League Baseball franchises. Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated. Team Revenue Value Baltimore 179 460 Boston 310 1000 Chicago White Sox 214 600 Cleveland 178 410 Detroit 217 478 Kansas City 161 354 Los Angeles Angels 226 656 Minnesota 213 510 New York Yankees 439 1850 Oakland 160 321 Seattle 210 585 Tampa Bay 161 323 Texas 233 674 Toronto 188 413 Arizona 186 447 Atlanta 203 508 Chicago Cubs 266 879 Cincinnati 185 424 Colorado 193 464 Houston 196 549 Los Angeles 230 1400 Miami 148 450 Milwaukee 195…
- A professor in the School of Business in a university polled a dozen colleagues about the number of professional meetings they attended in the past five years (x) and the number of papers they submitted to refereed journals (y) during the same period. The summary data are provided. Fit a simple linear regression model between x and y by finding out the estimates of intercept and slope. Comment on whether attending more professional meetings would result in publishing more papers. n n n = 12, x = 4, y = 12, X₁Y₁ = 320 i=1 x² = 234, i=1 The estimated regression line is y = 36.4 + (-6.10 )x. (Round to two decimal places as needed.) Comment on whether attending more professional meetings would result in publishing more papers. Let it be unclear that attending more professional meetings affects the number of published papers if the value used to make that determination is between 1 and 1. Because the of the regression equation is it would appear that attending more professional meetings ▼The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ý = 22.525 + 0.325x, where x = price ($) and y overall score. %3D Brand Price ($) Score 180 78 B. 150 71 C 95 59 70 54 E 70 40 35 28 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) SST SSR %3D SSE = (b) Compute the coefficient of determination . (Round your answer to three decimal places.) 1 = Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line. O The least squares line did not provide a good fit as a large proportion of the variability in y…i. Determine the dependent and independent variable ii. Based on the output, state the simple linear regression model. ii. Interpret the linear regression model obtained in part (b).
- A supermarket has a chain of 12 stores in Kuwait. Sales figures and profits for the stores are given in the following table. Obtain a regression equation for the data, and predict profit for a store assuming sales of $20 million. Show all calculations in detail. Sales, x (in millions of dollars) Profits, y (in millions of dollars) 7 0.12 2 0.1 6 0.13 12 0.15 14 0.25 16 0.2 10 0.24 12 0.2 14 0.27 20 0.15 7 0.34 8 0.17A study examined the eating habits of 20 children at a nursery school. The variables measured for each child included: calories (the number of calories eaten at lunch), time (the time in minutes spent eating lunch), and sex (male=1, female=0). A multiple linear regression model using Y = calories, X1 = time, and X2 = sex led to the following model: y=547.65-2.85x1+10.67x2 For two children who spend the same amount of time eating, one male and one female, which child is predicted to consume more calories and by how much?The value of a sports franchise is directly related to the amount of revenue that a franchise can generate. The following data represents the value in 2014 (in $millions) and the annual revenue (in $millions) for the 30 Major League Baseball franchises. Suppose you want to develop a simple linear regression model to predict franchise value based on annual revenue generated. Team Revenue Value Baltimore 245 1000 Boston 370 2100 Chicago White Sox 227 975 Cleveland 207 825 Detroit 254 1125 Houston 175 800 Kansas City 231 700 Los Angeles Angels 304 1300 Minnesota 223 895 New York Yankees 508 3200 Oakland 202 725 Seattle 250 1100 Tampa Bay 188 625 Texas 266 1220 Toronto 226 870 Arizona 211 840 Atlanta 267 1150 Chicago Cubs 302 1800 Cincinnati 227 885 Colorado…
- Write out the full linear model including all dummy variables below. Don’t worry about estimating regression coefficients just yet. Feel free to abbreviate variable names so long as they are clearly distinguishable.The following data show the brand, price ($), and the overall score for six stereo headphones that were tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is ŷ = 21.592 + 0.324x, where x = price ($) and y = overall score. Brand Price ($) Score A 180 76 B 150 69 C 95 61 D 70 56 E 70 38 F 35 24 (a) Compute SST, SSR, and SSE. (Round your answers to three decimal places.) (b) Compute the coefficient of determination r2. (Round your answer to three decimal places.) (c) What is the value of the sample correlation coefficient? (Round your answer to three decimal places.)The following table shows the approximate amount of trash produced in an industrialized country from 1980 to 2000. Let x represent the year after 1980 (1980 is year 0) and y represent the amount of trash (millions of tons). Year Million Tons 1980 150 1990 202 2000 220 (a) Draw the graph for this data. (b) Find the equation of the regression line for the data. (Round your answers to one decimal place.)y = x + (c) Use the equation to predict the amount of trash y that will be produced in 2010 and 2015. (Round your answers to one decimal place.) 2010: _______million tons 2015: _______ million tons
