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# Questions with answers for regression 1003

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This 8 page Study Guide was uploaded by Upasana Raja on Friday December 4, 2015. The Study Guide belongs to 1003 at a university taught by Jennifer in Fall 2015. Since its upload, it has received 307 views.

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Date Created: 12/04/15

CORRELATION amp REGRESSION M ULTI PLE CHOICE QUESTIONS In the followi ng multiplechoice questions select the best answer 1 The correlation coefficient is used to determine a A specific value of the yvariable given a specific value of the xvariable b A specific value of the xvariable given a specific value of the yvariable c The strength of the relationship between the x and y variables d None of these If there is avery strong correlation between two variables then the correlation coefficient must be a any value larger than 1 b much smaller than 0 if the correlation is negative c much larger than 0 regardless of whether the correlation is negative or positive d None of these alternatives is correct I n regression the equation that describes how the response variable y is related to the explanatory variable x is a the correl ati on model b the regression model c used to compute the correlation coefficient d None of these alternatives is correct The relationship between number of beers consumed x and blood alcohol content y was studied in 16 male college students by using least squares regression The following regression equation was obtained from this study T 00127 00180X The above equation impl ies that a each beer consumed increases blood alcohol by 127 b on average it takes 18 beers to increase blood alcohol content by 1 c each beer consumed increases blood alcohol by an average of amount of 18 d each beer consumed increases blood alcohol by exactly 0018 SSE can never be a larger than SST b smaller than SST c equal to 1 d equal to zero 10 11 Regression modeling is a statistical framework for developing a mathematical equation that describes how a one explanatory and one or more response variables are related b several explanatory and several response variables response are related c one response and one or more explanatory variables are related d All of these are correct In regression analysis the variable that is being predicted isthe a response or dependent variable b i ndependent variable c intervening variable d is usually x Regression analysis was applied to return rates of sparrowhawk colonies Regression analysiswas used to study the relationship between return rate x of bi rds that return to the colony in a given year and immigration rate y of new adults that join the colony per year The following regression equation was obtained 1 319 034x Based on the above estimated regression equation if the return rate were to decrease by 10 the rate of immigration to the colony would a increase by 34 b increase by 34 c decrease by 034 d decrease by 34 In least squares regression which of the following is not a required assumption about the error term a a The expected value of the error term is one b The variance of the error term is the same for all val ues of x c The values of the error term are independent d The error term is normally distributed Larger values of r2 R2 imply that the observations are more closely grouped about the a average val ue of the independent variables b average val ue of the dependent variable c least squares line d origin In a regression analysis if r2 1 then a SSE must also be equal to one b SSE must be equal to zero c SSE can be any positive val ue d SSE must be negative 12 13 14 15 16 17 The coefficient of correlation a is the square of the coefficient of determination b is the square root of the coefficient of determination c is the same as rsquare d can never be negative In regression analysis the variable that is used to explain the change in the outcome of an experiment or some natural process is cal led the xvari abl e the i ndependent variable the predictor variable the explanatory variable all of the above ad are correct none are correct op069 l n the case of an algebraic model for a straight line if a value for the x variable is specified then a the exact value of the response variable can be computed b the computed response to the independent value will always give a minimal residual c the computed val ue of y will always be the best estimate of the mean response d none of these alternatives is correct A regression analysis between sales in 1000 and price in dollars resulted in the following equation T 50000 8X The above equation impl ies that an a increaseof 1 in priceisassociated with adecreaseof 8in sales b increase of 8 in price is associated with an increase of 8000 in sales c increase of 1 in price is associated with adecrease of 42000 in sales d increase of 1 in price is associated with a decrease of 8000 in sales In a regression and correlation analysis if r2 1 then a SSE SST b SSE 1 c SSR SSE d SSR SST If the coefficient of determination is a positive value then the regression equation a must have a positive slope b must have a negative sl ope c could have either a positive or a negative slope d must have a positive y intercept 18 19 20 21 22 23 If two variables x and y have a very strong linear relationship then a there is evidence that x causes a change in y b there is evidence that y causes a change in x c there might not be any causal relationship between x and y d None of these alternatives is correct If the coefficient of determination is equal to 1 then the correlation coefficient a must also be equal to 1 b can be either 1 or 1 c can be any value between 1 to 1 d must be 1 In regression analysis if the independent variable is measured in kilograms the dependent variable a must also be in kilograms b must be in some unit of weight c cannot be in kilograms d can be any units The data are the same as for question 4 above The relationship between number of beers consumed x and blood alcohol content y was studied in 16 male college students by using least squares regression The followi ng regression equation was obtained from this study T 00127 00180X Supposethat the legal limit to drive is a blood alcohol content of 008 If Ricky consumed 5 beers the model would predict that he would be a 009 above the legal limit b 00027 below the legal limit c 00027 above the legal limit d 00733 above the legal limit In a regression analysis if SSE 200 and SSR 300 then the coefficient of determination is a 06667 b 06000 c 04000 d 1 5000 If the correlation coefficient is 08 the percentage of variation in the response variable expl ai ned by the variation in the explanatory variable is a 080 b 80 c 064 d 64 24 25 26 27 28 29 If the correlation coefficient is a positive value then the slope of the regression line a must also be positive b can be either negative or positive c can be zero d can not be zero If the coefficient of determination is 081 the correlation coefficient a is 06561 b could be either 09 or 09 c must be positive d must be negative A fitted least squares regression line a may be used to predict a value of y if the corresponding x value is given b is evidence for a causeeffect relationship between x and y c can only be computed if a strong linear relationship exists between x and y d None of these alternatives is correct Regression analysiswas applied between sales y and advertising x across all the branches of a major international corporation The following regression function was obtained T 5000 725X If the advertisi ng budgets of two branches of the corporation differ by 30000 then what will be the predicted difference in their sales a 21 7 500 b 222500 c 5000 d 725 Suppose the correl ati on coefficient between height as measured in feet versus weight as measured in pounds is 040 What isthe correlation coefficient of height measured in inches versus weight measured in ounces 12 inches one foot 16 ounces one pound a 040 b 030 c 0533 d cannot be determined from information given e none of these Assume the same variables as in question 28 above height is measured in feet and weight is measured in pounds Now suppose that the units of both variables are converted to metric meters and kilograms The impact on the slope is a the sign of the slope will change b the magnitude of the slope will change c both a and b are correct d neither a nor b are correct 30 31 32 33 Suppose that you have carried out a regression analysis where the total variance in the response is 133452 and the correlation coefficient was 085 The residual sums of squares is a 3703292 b 200178 c 1134342 d 9641907 e 15 f 015 This question is related to questions4 and 21 above The relationship between number of beers consumed x and blood alcohol content y was studied in 16 male college students by using least squares regression The followi ng regression equation was obtained from this study T 00127 00180x Another guy his name Dudley has the regression equation written on a scrap of paper in his pocket Dudley goes out drinking and has4 beers He calculates that he is under the legal limit 008 so he decides to drive to another bar Unfortunately Dudley gets pulled over and confidently submits to a roadsi de blood alcohol test He scores a blood alcohol of 0085 and gets himself arrested Obviously Dudley skipped the lecture about residual variation Dudley s residual is 0005 0005 00257 00257 9069 You have carried out a regression analysis but after thinking about the relationship between variables you have decided you must swap the explanatory and the response variables After refitting the regression model to the data you expect that a the value of the correlation coefficient will change b the value of SSE will change c the value of the coefficient of determination will change d the sign of the slope will change e nothing changes Suppose you use regression to predict the height of awoman s current boyfriend by using her own height as the explanatory variable Height was measured in feet from a sample of 100 women undergraduates and their boyfriends at Dal housie University Now suppose that the height of both the women and the men are converted to centimeters The impact of this conversion on the slope is a the sign of the slope wi ll change b the magnitude of the slope will change c both a and b are correct d neither a nor b are correct 34 A residual plot displays residuals of the explanatory variable versus residuals of the response variable displays residuals of the explanatory variable versus the response variable displays explanatory variable versus residuals of the response variable displays the explanatory variable versus the response variable displays the explanatory variable on the x axis versus the response variable on the y axis roe069 35 When the error terms have a constant variance a plot of the residuals versus the independent variable x has a pattern that fans out funnels in fans out but then funnels in forms a horizontal band pattern forms a linear pattern that can be positive or negative roe069 36 You studied the impact of the dose of a new drug treatment for high blood pressure You think that the drug might be more effective in people with very high blood pressure Because you expect a bigger change in those patients who start the treatment with high blood pressure you use regression to analyze the relationship between the initial blood pressure of a patient x and the change in blood pressure after treatment with the new drug y If you find avery strong positive association between these variables then a there is evidence that the higher the patients initial blood pressure the bigger the impact of the new drug b there is evidence that the higher the patients initial blood pressure the smaller the impact of the new drug c there is evidence for an association of some kind between the patients initial blood pressure and the impact of the new drug on the patients blood pressure d none of these are correct this is a case of regression fallacy Question 37 A variety of summary statisticswere collected for a small sample 10 of bivariate data where the dependent variable was y and an independent variable was x zx90 2Y lt 466 2Y170 zl lt X2234 n10 zlY V21434 SSE50598 371 Use the formula to the right to compute the sample correlation coefficient a 08045 in b 08045 L x c o Ell will t fl d 1 rs i5 u L 1 f E In Flil f I l i 372 373 374 375 376 The least squares estimate of b1 equals a 0923 b 1991 c 1991 d 0923 The least squares estimate of be equals a 0923 b 1991 c 1991 d 0923 The sum of squares due to regression SSR is a 1434 b 50598 0 50598 d 92802 The coefficient of determination equals a 06471 b 06471 c 0 d 1 The point estimate of y when x 055 is 017205 2018 10905 2018 017205 roe069 M ULTI PLE CHOICE ANSWERS AQWNQQ WN9 Q omO39momOO39O39o 11 b 21 b 12 b 22 b 13 e 23 d 14 a 24 a 15 d 25 b 16 d 26 a 17 c 27 a 18 c 28 a 19 b 29 b 20 d 30 a 31 32 33 34 35 36 371 a 372 b 373 d 374 d QQOQO39O 375 a 376 a

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