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Q:
A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called
a. an interaction
b. a constant variable
c. a category variable
d. a qualitative variable
Q:
In regression analysis, an outlier is an observation whose
a. mean is larger than the standard deviation
b. residual is zero
c. mean is zero
d. residual is much larger than the rest of the residual values
Q:
In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are
a. 47 and 3
b. 3 and 47
c. 2 and 43
d. 3 and 43
Q:
A regression model involved 5 independent variables and 126 observations. The critical value of tfor testing the significance of each of the independent variable's coefficients will have
a. 131 degrees of freedom
b. 125 degrees of freedom
c. 130 degrees of freedom
d. 4 degrees of freedom
Q:
In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The coefficient of determination is
a. 0.300
b. 0.192
c. 0.500
d. 0.700
Q:
For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is
a. 0.333
b. 0.275
c. 0.300
d. 0.75
Q:
As the goodness of fit for the estimated multiple regression equation increases,
a. the value of the adjusted multiple coefficient of determination decreases
b. the value of the regression equation's constant b0decreases
c. the value of the multiple coefficient of determination increases
d. the value of the correlation coefficient increases
Q:
If a qualitative variable has klevels, the number of dummy variables required isa. k-1b. kc. k+ 1d. 2k
Q:
Scott Bell Builders would like to predict the total number of labor hours spent framing a house based on the square footage of the house. The following data has been compiled on ten houses recently built.Square Footage (100s)Framing Labor HoursSquare Footage (100s)Framing Labor Hours20195272252117029240232203122523200322752623035260a. Develop the least-squares estimated regression equation that relates framing labor hours to house square footage.b. Use the regression equation developed in part (a) to predict framing labor hours when the house size is 3350 square feet.
Q:
Connie Harris, in charge of office supplies at First Capital Mortgage Corp., would like to predict the quantity of paper used in the office photocopying machines per month. She believes that the number of loans originated in a month influence the volume of photocopying performed. She has compiled the following recent monthly data:Number of Loans Originated in MonthSheets of Photocopy Paper Used (000's)45222513502460254021251635184025a. Develop the least-squares estimated regression equation that relates sheets of photocopy paper used to loans originated.b. Use the regression equation developed in part (a) to forecast the amount of paper used in a month when 42 loan originations are expected.c. Compute SSE, SST, and SSR.d. Compute the coefficient of determination r2. Comment on the goodness of fit.e. Compute the correlation coefficient.f. Compute the mean square error MSE.g. Compute the standard error of the estimate.h. Compute the estimated standard deviation of b1.i. Use the t test to test the following hypothesis ï¢1= 0 at ï¡= .05.j. Develop a 95% confidence interval estimate for ï¢1to test the hypothesis ï¢1= 0.k. Use the F test to test the hypothesis ï¢1= 0 at a .05 level of significance.l. Develop a 95% confidence interval estimate of the mean number of sheets of paper used when 38 mortgages are originated.m. Develop a 95% prediction interval estimate for the number of sheets of paper used when 38 mortgages are originated.
Q:
Data points having high leverage are oftena.residualsb.sum of squares errorc.influentiald.None of the other answers is correct.
Q:
An observation that has a strong effect on the regression results is called a(n)a.residualb.sum of squares errorc.influential observationd.None of the other answers is correct.
Q:
A data point (observation) that does not fit the trend shown by the remaining data is called a(n)a. residualb. outlierc. point estimated. None of the other answers is correct.
Q:
Compared to the confidence interval estimate for a particular value of y(in a linear regression model), the interval estimate for an average value of ywill be
a. narrower
b. wider
c. the same
d. Not enough information is given.
Q:
Refer to Exhibit 12-3. Using ï¡= 0.05, the critical tvalue for testing the significance of the slope is
a. 1.753
b. 2.131
c. 1.746
d. 2.120
Q:
Refer to Exhibit 12-3. The tstatistic for testing the significance of the slope is
a. 1.80
b. 1.96
c. 6.709
d. 0.555
Q:
Refer to Exhibit 12-3. The critical Fvalue at ï¡= 0.05 is
a. 3.59
b. 3.68
c. 4.45
d. 4.54
Q:
Refer to Exhibit 12-3. The Fstatistic computed from the above data is
a. 3
b. 45
c. 48
d. Not enough information is given to answer this question.
Q:
Exhibit 12-3Regression analysis was applied between sales data (in $1,000s) and advertising data (in $100s) and the following information was obtained. = 12 + 1.8xn= 17SSR = 225SSE = 75sb1= 0.2683Refer to Exhibit 12-3. Based on the above estimated regression equation, if advertising is $3,000, then the point estimate for sales (in dollars) isa. $66,000b. $5,412c. $66d. $17,400
Q:
In simple linear regression analysis, which of the following is not true?a. The Ftest and the ttest yield the same results.b. The Ftest and the ttest may or may not yield the same results.c. The relationship between xand yis represented by means of a straight line.d. The value of F= t2.
Q:
In regression analysis, which of the following is not a required assumption about the error term �
a. The expected value of the error term is zero.
b. The variance of the error term is the same for all values of x.
c. The values of the error term are independent.
d. All are required assumptions about the error term.
Q:
Refer to Exhibit 12-2. The coefficient of determination equals
a. -0.99705
b. -0.9941
c. 0.9941
d. 0.99705
Q:
Refer to Exhibit 12-2. The sample correlation coefficient equals
a. -86.667
b. -0.99705
c. 0.9941
d. 0.99705
Q:
Refer to Exhibit 12-2. The least squares estimate of b0equals
a. -7.647
b. -1.3
c. 21.4
d. 16.41176
Q:
Exhibit 12-2You are given the following information about yand x.yxDependent VariableIndependent Variable515712910117Refer to Exhibit 12-2. The least squares estimate of b1equalsa. -0.7647b. -0.13c. 21.4d. 16.412
Q:
Refer to Exhibit 12-1. The coefficient of determination equalsa. 0b. -1c. +1d. -0.5
Q:
Refer to Exhibit 12-1. The sample correlation coefficient equals
a. 0
b. -1
c. +1
d. -0.5
Q:
Refer to Exhibit 12-1. The point estimate of ywhen x= 20 is
a. 0
b. 31
c. 9
d. -9
Q:
Refer to Exhibit 12-1. The least squares estimate of b0equals
a. 1
b. -1
c. 5.5
d. 11
Q:
Exhibit 12-1A regression analysis resulted in the following information regarding a dependent variable (y) and an independent variable (x).n= 10x= 55y= 55x2= 385y2 = 385xy= 220Refer to Exhibit 12-1. The least squares estimate of b1equalsa. 1b. -1c. 5.5d. 11
Q:
If two variables, xand y, have a strong linear relationship, thena. there may or may not be any causal relationship between xand yb. xcauses yto happenc. ycauses xto happend. None of these answers is correct.
Q:
If the coefficient of determination is 0.81, the coefficient of correlation
a. is 0.6561
b. must be 0.9
c. must be positive
d. None of these answers is correct.
Q:
The numerical value of the coefficient of determination
a. is always larger than the coefficient of correlation
b. is always smaller than the coefficient of correlation
c. is negative if the coefficient of determination is negative
d. can be larger or smaller than the coefficient of correlation
Q:
If the coefficient of correlation is a negative value, then the coefficient of determination
a. must also be negative
b. must be zero
c. can be either negative or positive
d. must be positive
Q:
If the coefficient of correlation 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. None of these answers is correct.
Q:
If there is a very strong correlation between two variables, then the coefficient of correlation must be
a. much larger than 1, if the correlation is positive
b. much smaller than 1, if the correlation is negative
c. either much larger than 1 or much smaller than 1
d. None of these answers is correct.
Q:
If the coefficient of determination is equal to 1, then the coefficient of correlation
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
Q:
If the coefficient of correlation is 0.4, the percentage of variation in the dependent variable explained by the estimated regression equation
a. is 40%
b. is 16%
c. is 4%
d. can be any positive value
Q:
If the coefficient of correlation is 0.8, the percentage of variation in the dependent variable explained by the estimated regression equation is
a. 0.80%
b. 80%
c. 0.64%
d. 64%
Q:
It is possible for the coefficient of determination to be
a. larger than 1
b. less than one
c. less than zero
d. All of these answers are correct, depending on the situation under consideration.
Q:
If the coefficient of determination is a positive value, then the regression equation
a. must have a positive slope
b. must have a negative slope
c. could have either a positive or a negative slope
d. must have a positive y intercept
Q:
In a regression analysis if SST=4500 and SSE=1575, then the coefficient of determination is
a. 0.35
b. 0.65
c. 2.85
d. 0.45
Q:
If a data set has SST = 2,000 and SSE = 800, then the coefficient of determination is
a. 0.4
b. 0.6
c. 0.5
d. 0.8
Q:
In a regression analysis if SSE = 500 and SSR = 300, then the coefficient of determination is
a. 0.6000
b. 0.1666
c. 1.6666
d. 0.3750
Q:
In a regression analysis if SSE = 200 and SSR = 300, then the coefficient of determination is
a. 0.6667
b. 0.6000
c. 0.4000
d. 1.5000
Q:
In regression and correlation analysis, if SSE and SST are known, then with this information the
a. coefficient of determination can be computed
b. slope of the line can be computed
c. yintercept can be computed
d. All of the above can be computed.
Q:
In a regression analysis if r2= 1, then
a. SSE = SST
b. SSE = 1
c. SSR = SSE
d. SSR = SST
Q:
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 value
d. SSE must be negative
Q:
Larger values of r2imply that the observations are more closely grouped about the
a. average value of the independent variables
b. average value of the dependent variable
c. least squares line
d. origin
Q:
If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on this data isa. 0b. 1c. either 1 or -1, depending upon whether the relationship is positive or negatived. could be any value between -1 and 1
Q:
In simple linear regression, r2 is the
a. estimated regression equation
b. coefficient of correlation
c. sum of the squared residuals
d. coefficient of determination
Q:
Which of the following is correct?
a. SSE = SSR + SST
b. SSR = SSE + SST
c. SST = SSR + SSE
d. SST = (SSR)2
Q:
SSE can never be
a. larger than SST
b. smaller than SST
c. equal to 1
d. equal to zero
Q:
A regression analysis between sales (yin $1000) and advertising (xin dollars) resulted in the following equation = 50,000 + 6x
The above equation implies that an
a. increase of $6 in advertising is associated with an increase of $6,000 in sales
b. increase of $1 in advertising is associated with an increase of $6 in sales
c. increase of $1 in advertising is associated with an increase of $56,000 in sales
d. increase of $1 in advertising is associated with an increase of $6,000 in sales
Q:
A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation = 50,000 " 8x
The above equation implies that an
a. increase of $1 in price is associated with a decrease of $8 in sales
b. increase of $8 in price is associated with an increase of $8,000 in sales
c. increase of $1 in price is associated with a decrease of $42,000 in sales
d. increase of $1 in price is associated with a decrease of $8000 in sales
Q:
A regression analysis between demand (yin 1000 units) and price (xin dollars) resulted in the following equation = 9 " 3x
The above equation implies that if the price is increased by $1, the demand is expected to
a. increase by 6 units
b. decrease by 3 units
c. decrease by 6,000 units
d. decrease by 3,000 units
Q:
Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. = 500 + 4x
Based on the above estimated regression line if advertising is $10,000, then the point estimate for sales (in dollars) is
a. $900
b. $900,000
c. $40,500
d. $505,000
Q:
Regression analysis was applied between sales (in $1,000) and advertising (in $100), and the following regression function was obtained. = 80 + 6.2x
Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is
a. $62,080
b. $142,000
c. $700
d. $700,000
Q:
In regression analysis if the dependent variable is measured in dollars, the independent variable
a. must also be in dollars
b. must be in some unit of currency
c. can be any units
d. can not be in dollars
Q:
A least squares regression line
a. may be used to predict a value of yif the corresponding xvalue is given
b. implies a cause-effect relationship between xand y
c. can only be determined if a good linear relationship exists between xand y
d. All of these answers are correct.
Q:
Application of the least squares method results in values of the yintercept and the slope that minimizes the sum of the squared deviations between the
a. observed values of the independent variable and the estimated values of the independent variable
b. actual values of the independent variable and estimated values of the dependent variable
c. observed values of the dependent variable and the estimated values of the dependent variable
d. None of these answers is correct.
Q:
A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is the
a. correlation analysis
b. mean squares method
c. least squares method
d. most squares method
Q:
In a simple regression analysis (where yis a dependent and xan independent variable), if the yintercept is positive, then
a. there is a positive correlation between xand y
b. there is a negative correlation between xand y
c. if xis increased, ymust also increase
d. None of these answers is correct.
Q:
The equation that describes how the dependent variable (y) is related to the independent variable (x) is called
a. the correlation model
b. the regression model
c. correlation analysis
d. None of these answers is correct.
Q:
In regression analysis, the independent variable is
a. used to predict other independent variables
b. used to predict the dependent variable
c. called the intervening variable
d. None of these answers is correct.
Q:
In a regression analysis, the variable that is being predicted
a. must have the same units as the variable doing the predicting
b. is the independent variable
c. is the dependent variable
d. usually is denoted by x
Q:
In regression analysis, the variable that is being predicted is the
a. dependent variable
b. independent variable
c. intervening variable
d. None of these answers is correct.
Q:
Regression analysis is a statistical procedure for developing a mathematical equation that describes how
a. one independent and one or more dependent variables are related
b. several independent and several dependent variables are related
c. one dependent and one or more independent variables are related
d. None of these answers is correct.
Q:
The interval estimate of the mean value of yfor a given value of xis the
a. confidence interval
b. prediction interval
c. residual interval
d. correlation interval
Q:
A measure of the strength of the relationship between two variables is the
a. coefficient of determination
b. slope b1of the estimated regression line
c. standard error of the estimate
d. correlation coefficient
Q:
As the goodness of fit for the estimated regression equation increases,
a. the absolute value of the regression equation's slope increases
b. the value of the regression equation's yintercept decreases
c. the value of the coefficient of determination increases
d. the value of the correlation coefficient increases
Q:
The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is the
a. standard error
b. residual
c. prediction interval
d. variance
Q:
In a residual plot against xthat does notsuggest we should challenge the assumptions of our regression model, we would expect to see
a. a horizontal band of points centered near zero
b. a widening band of points
c. a band of points having a slope consistent with that of the regression equation
d. a parabolic band of points
Q:
The least squares criterion is
a. min b. min c. min d. min
Q:
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the
a. correlation coefficient
b. standard error of the estimate
c. coefficient of determination
d. confidence interval estimate
Q:
Employee panel preferences for three proposed company logo designs follow.Logo DesignABCNumber of Employees Preferring Design785966Use = .05 and test to determine any difference in preference among the three logo designs.
Q:
A movie based on a best-selling novel was recently released. Six hundred viewers of the movie, 235 of whom had previously read the novel, were asked to rate the quality of the movie. The survey showed that 141 of the novel readers gave the movie a rating of excellent, while 248 of the non-readers gave the movie an excellent rating.a. Develop an interval estimate of the difference between the proportions of the two populations, using a .05 level of significance, as the basis for your decision.b. Can we conclude, on the basis of a hypothesis test about p1" p2, that the proportion of the non-readers of the novel who thought the movie was excellent is greater than the proportion of readers of the novel who thought the movie was excellent?Use a .05 level of significance. (Hint: this is a one-tailed test.)
Q:
A study of wage discrimination at a local store compared employees' race and their status. Partial results of the study follow. Use Excel and test at = .05 to determine if gender is independent of status.WorkerRaceStatusWorkerRaceStatus1whitemanager26non-whiteassociate2non-whiteassociate27whitedistrict manager3whitedistrict manager28non-whitemanager4whitemanager29whiteassociate5whitemanager30non-whitedistrict manager6non-whiteassociate31non-whitedistrict manager7non-whiteassociate32whitedistrict manager8whiteassociate33whitedistrict manager9non-whiteassociate34non-whiteassociate10whitemanager35whitedistrict manager11non-whitemanager36non-whiteassociate12non-whiteassociate37non-whitemanager13whiteassociate38non-whiteassociate14non-whiteassociate39whitedistrict manager15whitedistrict manager40non-whiteassociate16whitedistrict manager41non-whitemanager17non-whiteassociate42non-whitedistrict manager18non-whiteassociate43whitemanager19whiteassociate44whitedistrict manager20non-whitemanager45non-whiteassociate21whitedistrict manager46non-whiteassociate22non-whitedistrict manager47non-whitedistrict manager23non-whitemanager48whitemanager24non-whiteassociate49non-whitemanager25non-whiteassociate50non-whiteassociate
Q:
Members of a focus group stated their preferences between three possible slogans. The results follow. Use Excel to test at = .05 to determine any difference in preference among the three slogans.Slogan PreferencesAACCBCBBAABCABCCCCBBCBCCAAACAB
Q:
During "sweeps week" last year, the viewing audience was distributed as follows: 36% NBC, 22% ABC, 24% CBS, and 18% FOX. This year during "sweeps week" a sample of 50 homes yielded the following data. Use Excel to test at ï¡= .05 to determine if the audience proportions have changed.ABCFOXABCFOXABCABCCBSNBCFOXFOXNBCABCCBSABCNBCNBCNBCCBSFOXABCABCFOXNBCCBSCBSNBCNBCABCFOXFOXNBCNBCNBCNBCFOXABCFOXNBCFOXCBSCBSCBSFOXFOXNBCCBSFOXCBSFOXNBC