Q&A Hero

Q: Jim Royo, manager of Billings Building Supply (BBS), wants to develop a model to forecast BBS's monthly sales (in $1,000's). He selects the dollar value of residential building permits (in $10,000) as the predictor variable. An analysis of the data yielded the following tables. CoefficientsStandard Errort Statisticp-valueIntercept222.145674.7652.9712520.007284x6.1528851.8954233.246180.003866 dfSSMSFp-valueRegression1259643.9259643.910.537680.004046Residual20492791.324639.56 Total21752435.2 Jim's calculated value for the Durbin-Watson statistic is 1.14. Using a= 0.05, the appropriate decision is: _________.a) do not reject H0: r= 0b) reject H0: r= 0c) do not reject H0: r 0d) the test is inconclusivee) reject H0: r 0

Q: Jim Royo, manager of Billings Building Supply (BBS), wants to develop a model to forecast BBS's monthly sales (in $1,000's). He selects the dollar value of residential building permits (in $10,000) as the predictor variable. An analysis of the data yielded the following tables. CoefficientsStandard Errort Statisticp-valueIntercept222.145674.7652.9712520.007284x6.1528851.8954233.246180.003866 dfSSMSFp-valueRegression1259643.9259643.910.537680.004046Residual20492791.324639.56 Total21752435.2 Jim's calculated value for the Durbin-Watson statistic is 1.93. Using a= 0.05, the appropriate decision is: _________.a) do not reject H0: r= 0b) reject H0:r 0c) do not reject: r 0d) the test is inconclusivee) reject H0: r= 0

Q: Jim Royo, manager of Billings Building Supply (BBS), wants to develop a model to forecast BBS's monthly sales (in $1,000's). He selects the dollar value of residential building permits (in $10,000) as the predictor variable. An analysis of the data yielded the following tables. Coefficients Standard Error t Statistic p-value Intercept 222.1456 74.765 2.971252 0.007284 x 6.152885 1.895423 3.24618 0.003866 df SS MS F p-value Regression 1 259643.9 259643.9 10.53768 0.004046 Residual 20 492791.3 24639.56 Total 21 752435.2 Using a= 0.05 the critical value of the Durbin-Watson statistic, dU,is _________. a) 1.54 b) 1.42 c) 1.43 d) 1.44 e) 1.85

Q: Jim Royo, manager of Billings Building Supply (BBS), wants to develop a model to forecast BBS's monthly sales (in $1,000's). He selects the dollar value of residential building permits (in $10,000) as the predictor variable. An analysis of the data yielded the following tables. Coefficients Standard Error t Statistic p-value Intercept 222.1456 74.765 2.971252 0.007284 x 6.152885 1.895423 3.24618 0.003866 df SS MS F p-value Regression 1 259643.9 259643.9 10.53768 0.004046 Residual 20 492791.3 24639.56 Total 21 752435.2 Using a= 0.05 the critical value of the Durbin-Watson statistic, dL,is _________. a) 1.24 b) 1.22 c) 1.13 d) 1.15 e) 1.85

Q: Analysis of data for an autoregressive forecasting model produced the following tables. Coefficients Standard Error t Statistic p-value Intercept 3.85094 3.745787 0.84426 0.34299 yt-1 0.70434 0.082849 -1.66023 0.103822 yt-2 -0.62669 0.035709 14.65044 6.69E-19 df SS MS F p-value Regression 2 135753.5 67876.76 107.3336 1.91E-17 Residual 43 27192.79 632.3904 Total 45 162946.3 The actual values of this time series, y, were 228, 54, and 191 for May, June, and July, respectively. The predicted (forecast) value for August is __________. a) -101.00 b) 104.54 c) 218.71 d) 21.56 e) -77.81

Q: Analysis of data for an autoregressive forecasting model produced the following tables. Coefficients Standard Error t Statistic p-value Intercept 3.85094 3.745787 0.84426 0.34299 yt-1 0.70434 0.082849 -1.66023 0.103822 yt-2 -0.62669 0.035709 14.65044 6.69E-19 df SS MS F p-value Regression 2 135753.5 67876.76 107.3336 1.91E-17 Residual 43 27192.79 632.3904 Total 45 162946.3 The actual values of this time series, y, were 228, 54, and 191 for May, June, and July, respectively. The forecast value predicted by the model for July is __________. a) -101.00 b) 104.54 c) 218.71 d) 21.56 e) -77.81

Q: Analysis of data for an autoregressive forecasting model produced the following tables. Coefficients Standard Error t Statistic p-value Intercept 3.85094 3.745787 0.84426 0.34299 yt-1 0.70434 0.082849 -1.66023 0.103822 yt-2 -0.62669 0.035709 14.65044 6.69E-19 df SS MS F p-value Regression 2 135753.5 67876.76 107.3336 1.91E-17 Residual 43 27192.79 632.3904 Total 45 162946.3 The results indicate that __________. a) the first predictor, yt-1, is significant at the 10% level b) the second predictor, yt-2, is significant at the 1% level c) all predictor variables are significant at the 5% level d) none of the predictor variables are significant at the 5% level e) the overall regression model is not significant at 5% level

Q: Analysis of data for an autoregressive forecasting model produced the following tables. Coefficients Standard Error t Statistic p-value Intercept 3.85094 3.745787 0.84426 0.34299 yt-1 0.70434 0.082849 -1.66023 0.13822 yt-2 -0.62669 0.035709 14.65044 6.69E-19 df SS MS F p-value Regression 2 135753.5 67876.76 107.3336 1.91E-17 Residual 43 27192.79 632.3904 Total 45 162946.3 The forecasting model is __________. a) yt= 3.745787 + 0.082849yt-1+ 0.035709yt-2 b) yt= 3.85094 + 0.70434yt-1- 0.62669yt-2 c) yt= 0.84426 - 1.66023yt-1+ 14.65023yt-2 d) yt= 0.34299 + 0.13822yt-1+ 9.69yt-2 e) yt= 0.34299 + 0.13822yt-1- 6.69yt-2

Q: In an autoregressive forecasting model, the independent variable(s) is (are) ______. a) time-lagged values of the dependent variable b) first-order differences of the dependent variable c) second-order, or higher, differences of the dependent variable d) first-order quotients of the dependent variable e) time-lagged values of the independent variable

Q: The ratios of "actuals to moving averages" (seasonal indexes) for a time series are presented in the following table as percentages. 2008 2009 2010 2011 2012 Q1 112.22 110.78 111.22 111.87 Q2 100.65 108.68 103.78 101.95 Q3 97.76 99.08 97.68 97.61 Q4 86.61 95.00 94.64 92.92 The final (completely adjusted) estimate of the seasonal index for Q1is __________. a) 109.733 b) 109.921 c) 113.853 d) 113.492 e) 111.545

Q: The high and low values of the "ratios of actuals to moving average" are ignored when finalizing the seasonal index for a period (month or quarter) in time series decomposition. The rationale for this is to ________. a) reduce the sample size b) eliminate autocorrelation c) minimize serial correlation d) eliminate the irregular component e) eliminate the trend

Q: Calculating the "ratios of actuals to moving average" is a common step in time series decomposition. The results (the quotients) of this step estimate the ________. a) trend and cyclical components b) seasonal and irregular components c) cyclical and irregular components d) trend and seasonal components e) irregular components

Q: Which of the following is not a component of time series data? a) Trend b) Seasonal fluctuations c) Cyclical fluctuations d) Normal fluctuations e) Irregular fluctuations

Q: Fitting a linear trend to 36 monthly data points (January 2011 = 1, February 2011 =2, March 2011 = 3, etc.) produced the following tables. Coefficients Standard Error t Statistic p-value Intercept 877.621 67.35824 13.02916 5.49E-15 x -9.00907 3.17471 -2.83776 0.00751 df SS MS F p-value Regression 1 315319.3 315319.3 8.052885 0.007607 Residual 34 1331306 39156.07 Total 35 1646626 The projected trend value for January 2014 is ________. a) 544.29 b) 868.61 c) 652.39 d) 760.50 e) 876.90

Q: Fitting a linear trend to 36 monthly data points (January 2011 = 1, February 2011 =2, March 2011 = 3, etc.) produced the following tables. Coefficients Standard Error t Statistic p-value Intercept 222.379 67.35824 3.301438 0.002221 x 9.009066 3.17471 2.83776 0.00751 df SS MS F p-value Regression 1 315319.3 315319.3 8.052885 0.007607 Residual 34 1331306 39156.07 Total 35 1646626 The projected trend value for January 2014 is ________. a) 231.39 b) 555.71 c) 339.50 d) 447.76 e) 355.71

Q: The following graph of a time-series data suggests a _______________ trend.a) linearb) quadraticc) cosined) tangentiale) flat

Q: The following graph of a time-series data suggests a _______________ trend.a) linearb) tangentialc) cosined) quadratice) flat

Q: The following graph of time-series data suggests a _______________ trend.a) linearb) quadraticc) cosined) tangentiale) flat

Q: The forecast value for September 21.1 and the actual value turned out to be 18. Using exponential smoothing with a= 0.30, the forecast value for October would be ______. a) 18.09 b) 18.93 c) 20.17 d) 21.00 e) 17.07

Q: The forecast value for August was 22 and the actual value turned out to be 19. Using exponential smoothing with a= 0.30, the forecast value for September would be ______. a) 21.1 b) 19.9 c) 18.1 d) 22.9 e) 21.0

Q: What is the forecast for the Period 7 using a 3-period moving average technique, given the following time-series data for six past periods? Period 1 2 3 4 5 6 Value 136 126 146 148 156 164 a) 164.67 b) 156.00 c) 148.00 d) 126.57 e) 158.67

Q: The city golf course is interested in starting a junior golf program. The golf pro has collected data on the number of youths under 13 that have played golf during the last 4 months. Using a three-month moving average (with weights of 5, 3, and 1 for the most current value, next most current value and oldest value, respectively), the forecast value for November in the following time series would be ____________. July 28 Aug 27 Sept 17 Oct 19 a) 24 b) 21 c) 21.56 d) 19.22 e) 22

Q: The city golf course is interested in starting a junior golf program. The golf pro has collected data on the number of youths under 13 that have played golf during the last 4 months. Using a three-month moving average (with weights of 5, 3, and 1 for the most current value, next most current value and oldest value, respectively), the forecast value for October made at the end of September in the following time series would be __________. July 28 Aug 27 Sept 17 Oct 19 a) 24 b) 21 c) 21.56 d) 19.22 e) 22

Q: The city golf course is interested in starting a junior golf program. The golf pro has collected data on the number of youths under 13 that have played golf during the last 4 months. Using a three-month moving average, the forecast value for November in the following time series would be ____________. July 28 Aug 27 Sept 17 Oct 19 a) 24 b) 21 c) 21.56 d) 19.22 e) 22

Q: The city golf course is interested in starting a junior golf program. The golf pros has collected data on the number of youths under 13 that have played golf during the last 4 months. Using a three-month moving average, the forecast value for October made at the end of September in the following time series would be ____________. July 28 Aug 27 Sept 17 Oct 19 a) 24 b) 21 c) 21.56 d) 19.22 e) 22

Q: Using a three-month moving average (with weights of 6, 3, and 1 for the most current value, next most current value and oldest value, respectively), the forecast value for November in the following time series is ____________. July 5 Aug 11 Sept 13 Oct 6 a) 11.60 b) 10.00 c) 9.67 d) 8.06 e) 8.60

Q: Using a three-month moving average (with weights of 6, 3, and 1 for the most current value, next most current value and oldest value, respectively), the forecast value for October made at the end of September in the following time series would be__________. July 5 Aug 11 Sept 13 Oct 6 a) 11.60 b) 10.00 c) 9.67 d) 8.60 e) 6.11

Q: Using a three-month moving average, the forecast value for November in the following time series is ____________. July 5 Aug 11 Sept 13 Oct 6 a) 11.60 b) 10.00 c) 9.67 d) 8.60 e) 6.00

Q: Using a three-month moving average, the forecast value for October made at the end of September in the following time series would be ____________. July 5 Aug 11 Sept 13 Oct 6 a) 11.60 b) 10.00 c) 9.07 d) 8.06 e) 9.67

Q: When forecasting with exponential smoothing, data from previous periods is _________. a) given equal importance b) given exponentially increasing importance c) ignored d) given exponentially decreasing importance e) linearly decreasing importance

Q: Use of a smoothing constant value less than 0.5 in an exponential smoothing model gives more weight to ___________. a) the actual value for the current period b) the actual value for the previous period c) the forecast for the current period d) the forecast for the previous period e) the forecast for the next period

Q: Use of a smoothing constant value greater than 0.5 in an exponential smoothing model gives more weight to ___________. a) the actual value for the current period b) the actual value for the previous period c) the forecast for the current period d) the forecast for the previous period e) the forecast for the next period

Q: In exponential smoothing models, the value of the smoothing constant may be any number between ___________. a) -1 and 1 b) -5 and 5 c) 0 and 1 d) 0 and 10 e) 0 and 100

Q: A time series analysis was performed to determine the number of new online customers that joined the "˜Jelly of the Month Club". The actual number of new customers, the forecast values and error terms is presented in the following table. The mean squared error (MSE) for this forecast is ___________. Month Actual Forecast Error July 4 Aug 6 5 -1 Sept 3 6 3 Oct 9 8 -1 Nov 8 9 1 a) -0.50 b) 0.50 c) 1.50 d) 7.00 e) 3.00

Q: A time series analysis was performed to determine the number of new online customers that joined the "˜Jelly of the Month Club". The actual number of new customers, the forecast values and error terms is presented in the following table. The mean absolute deviation (MAD) for this forecast is ___________. Month Actual Forecast Error July 4 Aug 6 5 -1 Sept 3 6 3 Oct 9 8 -1 Nov 8 9 1 a) -0.50 b) 0.50 c) 1.50 d) 7.00 e) 3.00

Q: A time series analysis was performed to determine the number of new online customers that joined the "˜Jelly of the Month Club". The actual number of new customers, the forecast values and error terms is presented in the following table. The mean error (ME) for this forecast is ___________. Month Actual Forecast Error July 4 Aug 6 5 -1 Sept 3 6 3 Oct 9 8 -1 Nov 8 9 1 a) -0.50 b) 0.50 c) 1.50 d) 7.00 e) 3.00

Q: A time series with forecast values and error terms is presented in the following table. The mean squared error (MSE) for this forecast is ___________. Month Actual Forecast Error July 5 Aug 11 5 6.00 Sept 13 6.8 6.20 Oct 6 8.66 -2.66 Nov 5 7.862 -2.86 a) 13.33 b) 17.94 c) 89.71 d) 22.43 e) 32.34

Q: A time series with forecast values and error terms is presented in the following table. The mean absolute deviation (MAD) for this forecast is ___________. Month Actual Forecast Error July 5 Aug 11 5 6.00 Sept 13 6.8 6.20 Oct 6 8.66 -2.66 Nov 5 7.862 -2.86 a) 3.54 b) 7.41 c) 4.43 d) 17.72 e) 4.34

Q: A time series with forecast values and error terms is presented in the following table. The mean error (ME) for this forecast is ___________. Month Actual Forecast Error July 5 Aug 11 5 6.00 Sept 13 6.8 6.20 Oct 6 8.66 -2.66 Nov 5 7.862 -2.86 a) 1.67 b) 1.34 c) 6.68 d) 3.67 e) 2.87

Q: Unweighted price indexes compare across the entire time period for which there is data.

Q: A small value of the Durbin"Watson statistic indicates that successive error terms are positively correlated.

Q: In statistics, the Winters' Three Parameter statistic is a test statistic used to detect the presence of autocorrelation in the residuals from a regression analysis.

Q: Autocorrelation in a regression forecasting model can be detected by the Ftest.

Q: 21. Autoregression is a multiple regression technique in which the independent variables are time-lagged versions of the dependent variable.

Q: One of the ways to overcome the autocorrelation problem in a regression forecasting model is to transform the variables by taking the first-differences.

Q: One of the ways to overcome the autocorrelation problem in a regression forecasting model is to increase the level of significance for the Ftest

Q: If autocorrelation occurs in regression analysis, then the confidence intervals and tests using the t and F distributions are no longer strictly applicable.

Q: When the error terms of a regression forecasting model are correlated the problem of autocorrelation occurs.

Q: One of the main techniques for isolating the effects of seasonality is decomposition.

Q: One of the main techniques for isolating the effects of seasonality is reconstitution.

Q: If the trend equation is linear in time, the slope indicates the increase, or decrease when negative, in the forecasted value of the response value Y for the next time period.

Q: If the trend equation is quadratic in time t=1… .T, the forecast value for the next time T+1 depends on time T.

Q: Although seasonal effects can confound a trend analysis, a regression model is robust to these effects and the researcher does not need to adjust for seasonality prior to using a regression model to analyze trends.

Q: Linear regression models cannot be used to analyze quadratic trends in time-series data.

Q: An exponential smoothing technique in which the smoothing constant alpha is equal to one is equivalent to a regression forecasting model.

Q: Two popular general categories of smoothing techniques are exponential models and logarithmic models.

Q: Two popular general categories of smoothing techniques are averaging models and exponential models.

Q: When a trucking firm uses the number of shipments for January of the previous year as the forecast for January next year, it is using a nave forecasting model.

Q: Nave forecasting models have no useful applications because they do not take into account data trend, cyclical effects or seasonality.

Q: For large datasets, the mean error (ME) and mean absolute deviation (MAD) always have the same numerical value.

Q: Forecast error is the difference between the value of the response variable and those of the explanatory variables.

Q: A stationary time-series data has only trend but no cyclical or seasonal effects.

Q: The long-term general direction of data is referred to as series.

Q: Time-series data are data gathered on a desired characteristic at a particular point in time.

Q: A research project was conducted to study the effect of smoking and weight upon resting pulse rate. The response variable is coded as 1 when the pulse rate is low and 0 when it high. Smoking is also coding as 1 when smoking and 0 when not smoking. Shown below is Minitab output from a logistic regression.The predicted probability that a 150 pounds person who does not smoke has a low pulse rate isa) 0.639512b) 0.853987c) 0.2145d) 0.5e) 0.9871

Q: A research project was conducted to study the effect of smoking and weight upon resting pulse rate. The response variable is coded as 1 when the pulse rate is low and 0 when it high. Smoking is also coding as 1 when smoking and 0 when not smoking. Shown below is Minitab output from a logistic regression.The predicted probability that a 150 pounds person who smokes has a low pulse rate isa) 0.639512b) 0.853987c) 0.2145d) 0.5e) 0.9871

Q: Suppose a community based political group is interested in determining if there is a relationship between the years that a candidate lives in a community, the number of volunteer hours the candidate gives to the community, and the outcome of the candidate in the local city council election. Which of the following statements is not true about the experimental design. a) The election outcome (win/ lose) is the response variable.b) The number of hours the candidate gives in volunteering is the dependent variable.c) A correlation analysis should evaluate possible multicollinearity between the years a candidate lives in a community and the number of volunteer hours.d) The number of years a candidate lives in a community is an independent variable.e) The only variable that must be recoded 0 or 1 is the response variable.

Q: If a qualitative variable has "c" categories, how many dummy variables must be created and used in the regression analysis?a) c - 1b) cc) c + 1d) c - 2e) 4 +

Q: A research project was conducted to study the effect of smoking and weight upon resting pulse rate. The response variable is coded as 1 when the pulse rate is low and 0 when it high. Smoking is also coding as 1 when smoking and 0 when not smoking. Shown below is Minitab output from a logistic regression.The log of the odds ratio or logit equation is:a) log(S)=-1.19297+0.0250226 Weight-1.98717 Smokesb) S=-1.98717+0.025226 Weight-1.19297 Smokesc) Rating Pulse=-1.98717+0.025226 Weight-1.19297 Smokesd) log(S) =-1.98717+0.025226 Weight-1.19297 Smokese) log(p)=-1.98717+0.025226 Weight-1.19297 Smokes

Q: Suppose a company is interested in understanding the effect of age and gender on the likelihood a customer will purchase a new product. The data analyst intends to run a logistic regression on her data. Which of the following variable(s) will the analyst need to code as 0 or 1 prior to performing the logistic regression analysis?a) age and genderb) age and purchase statusc) aged) purchase statuse) gender and purchase status

Q: Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. y x1 x2 x3 x4 x5 y 1 x1 0.854168 1 x2 -0.11828 -0.00383 1 x3 -0.12003 -0.08499 -0.14523 1 x4 0.525901 0.118169 -0.14876 0.050042 1 x5 -0.18105 -0.07371 0.995886 -0.14151 -0.16934 1 a) x1 and x2 b) x1 and x5 c) x3 and x4 d) x2 and x5 e) x3 and x5

Q: Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. y x1 x2 x3 x4 x5 y 1 x1 -0.08301 1 x2 0.236745 -0.51728 1 x3 0.155149 -0.22264 -0.00734 1 x4 0.022234 -0.58079 0.884216 0.131956 1 x5 0.4808 -0.20467 0.078916 0.207477 0.103831 1 a) x1 and x5 b) x2 and x3 c) x4 and x2 d) x4 and x3 e) x4 and y

Q: Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals potential multicollinearity with variables ___________. y x1 x2 x3 x4 x5 y 1 x1 -0.0857 1 x2 -0.20246 0.868358 1 x3 -0.22631 -0.10604 -0.14853 1 x4 -0.28175 -0.0685 0.41468 -0.14151 1 x5 0.271105 0.150796 0.129388 -0.15243 0.00821 1 a) x1 and x2 b) x1 and x4 c) x4 and x5 d) x4 and x3 e) x5 and y

Q: A useful technique in controlling multicollinearity involves the _________. a) use of variance inflation factors b) use the backward elimination procedure c) use the forward elimination procedure d) use the forward selection procedure e) use all possible regressions

Q: An acceptable method of managing multicollinearity in a regression model is the ___. a) use the forward selection procedure b) use the backward elimination procedure c) use the forward elimination procedure d) use the stepwise regression procedure e) use all possible regressions

Q: An appropriate method to identify multicollinearity in a regression model is to ____. a) examine a residual plot b) examine the ANOVA table c) examine a correlation matrix d) examine the partial regression coefficients e) examine the R2 of the regression model

Q: Large correlations between two or more independent variables in a multiple regression model could result in the problem of ________. a) multicollinearity b) autocorrelation c) partial correlation d) rank correlation e) non-normality

Q: Carlos Cavazos, Director of Human Resources, is exploring employee absenteeism at the Plano Piano Plant. A multiple regression analysis was performed using the following variables. The results are presented below. Variable Description Y number of days absent last fiscal year x1 commuting distance (in miles) x2 employee's age (in years) x3 single-parent household (0 = yes, 1 = no) x4 length of employment at PPP (in years) x5 shift (0 = day, 1 = night) Coefficients Standard Error t Statistic p-value Intercept 6.594146 3.273005 2.014707 0.047671 x1 -0.18019 0.141949 -1.26939 0.208391 x2 0.268156 0.260643 1.028828 0.307005 x3 -2.31068 0.962056 -2.40182 0.018896 x4 -0.50579 0.270872 -1.86725 0.065937 x5 2.329513 0.940321 2.47736 0.015584 df SS MS F p-value Regression 5 279.358 55.8716 4.423755 0.001532 Residual 67 846.2036 12.6299 Total 72 1125.562 R = 0.498191 R2 = 0.248194 Adj R2 = 0.192089 se = 3.553858 n = 73 Which of the following conclusions can be drawn from the above results? a) All the independent variables in the regression are significant at 5% level. b) Commuting distance is a highly significant (<1%) variable in explaining absenteeism. c) Age of the employees tends to have a very significant (<1%) effect on absenteeism. d) This model explains a little over 49% of the variability in absenteeism data. e) A single-parent household employee is expected to be absent less number of days all other variables held constant compared to one who is not a single-parent household.

Q: Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals that the first independent variable that will be entered into the regression model by the forward selection procedure will be ___________. y x1 x2 x3 x4 x5 y 1 x1 0.854168 1 x2 -0.11828 -0.00383 1 x3 -0.12003 -0.08499 -0.14523 1 x4 0.525901 0.118169 -0.14876 0.050042 1 x5 -0.18105 -0.07371 0.995886 -0.14151 -0.16934 1 a) x1 b) x2 c) x3 d) x4 e) x5

Q: Inspection of the following table of correlation coefficients for variables in a multiple regression analysis reveals that the first independent variable that will be entered into the regression model by the forward selection procedure will be ___________. y x1 x2 x3 x4 x5 y 1 x1 -0.0857 1 x2 -0.20246 0.868358 1 x3 -0.22631 -0.10604 -0.14853 1 x4 -0.28175 -0.0685 0.41468 -0.14151 1 x5 0.271105 0.150796 0.129388 -0.15243 0.00821 1 a) x1 b) x2 c) x3 d) x4 e) x5