What is meant when a statistician talks about getting a "best fit" least squares regression line (hint: what is the mathematical relationship behind this?)
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What is meant when a statistician talks about getting a "best fit" least squares regression line (hint: what is the mathematical relationship behind this?)
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- An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. LOADING... Click here to view the weight and gas mileage data. Question content area bottom Part 1 (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. ModifyingAbove y with caretyequals=enter your response herexplus+(enter your response here) (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.)Is It Getting Harder to Win a Hot Dog Eating Contest?Every Fourth of July, Nathan’s Famous in New York City holds a hot dog eating contest. The table below shows the winning number of hot dogs and buns eaten every year from 2002 to 2015, and the data are also available in HotDogs. The figure below shows the scatterplot with the regression line. Year Hot Dogs 2015 62 2014 61 2013 69 2012 68 2011 62 2010 54 2009 68 2008 59 2007 66 2006 54 2005 49 2004 54 2003 45 2002 50 Winning number of hot dogs in the hot dog eating contest Winning number of hot dogs and buns Click here for the dataset associated with this question. (a) Is the trend in the data mostly positive or negative? Positive Negative (b) Using the figure provided, is the residual larger in 2007 or 2008?Choose the answer from the menu in accordance to item (b) of the question statement 20072008 Is the residual positive or…2.1. Give one word for the following statements or scenarios: 2.1.1. The data collected by the researcher from the Department of Education were the 2020 matric results for all South African high schools in disadvantaged areas.. 2.1.2. This analysis can be performed using either the method of moving averages, or by fitting a straight line using the method of least squares from regression analysis.
- A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the accompanying data. Complete parts (a) through (g) below. Click the icon to view the children's data. (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. y=x+ (Round the slope to three decimal places and round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. First interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. For every inch increase in head circumference, the height increases by in., on average. (Round to three decimal places as needed.) OB. For a height of 0 inches, the head circumference is predicted to be in. (Round to three decimal places as…From the parameter estimation output, which of the following is FALSE? Coefficients Standard Error t Stat p-value 0.783 0.0159 Intercept Diameter (mm) of granules of sand -2.476 -3.161 17.159 2.034 8.438 0.000065 For a one-unit increase in the independent variable, the predicted-y is decrease by – 2.476. The independent variable is significant. For a one-unit increase in the independent variable, the predicted-y is increase by 17.159. The predictor variable is significant.True or False? The r2 value and a least squares regression line can be an excellent way to demonstrate the degree of correlation between two variables, and the type of association between the two variables. This quation was asked twice in bartley but the answers were different. Clarification is needed. Thank you
- A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the accompanying data. Complete parts (a) through (g) below. Click the icon to view the children's data. Data table (a) Find the least-squares regression line treating height y =x+ (O (Round the slope to three decimal places and round the d Height (inches), x Head Circumference (inches), y O. 28 17.6 24.5 17.1 25.75 17.1 25.75 17.5 24.25 17.0 27.75 17.7 26.5 17.3 27.25 17.6 26.5 17.3 26.5 17.5 27.75 17.6 Print Done Help me solve this View an example Get more help - Media - Clear all Check answerA 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…At Hard Rock’s Moscow restaurant, the manager is trying to evaluate how a new advertising campaign affects guest counts. Using data for the past 10 months (see the table), develop a least-squares regression relationship and then forecast the expected guest count when advertising is $65,000.
- A chemical engineer is investigating the effect of process operating temperature on product yield. The study results in the following data: Temperature Yield 100 57.71 110 63.17 120 76.30 130 73.30 140 89.07 150 91.17 160 170 114.11 106.33 180 190 114.38 124.07 You can use Minitab to answer the following questions. However, you should be able to calculate the slope and intercept of the least squares regression model by hand, which requires only the mear and standard deviations of X and Y, and the correlation coefficient (here r = 0.9751). 1. what is the mean temperature? 155 150 130 145 Submit Answer Tries 0/2Absences and Final Exam Scores No. of absences, x 0 1 For students WHO IIISS THO Classes is et the slope or the y-intercept. = as needed.) Final exam score, y 88.9 86.6 83.6 81.5 student who misses five class periods. 2 Print 3 = needed.) ow average for this number of absences? 4 5 78.2 73.7 Done 6 7 8 63.9 72.7 It is not appropriate to interpret the slope. 9 65.3 65.4 0 O X Reference 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.997 0.950 0.878 0.811 0.754 0.707 0.666 0.632 0.602 0.576 0.553 0.532 0.514 0.497 0.482 0.468 0.456 0.444