Please complete the attached Basic Estimation Technique Finance questions

Chapter 4: BASIC ESTIMATION TECHNIQUES Multiple Choice a. b. c. d. e. 4-1 For the equation Y = a + bX, the objective of regression analysis is to estimate the parameters a and b. estimate the variables Y and X. fit a straight line through the data scatter in such a way that the sum of the squared errors is minimized. both a and c all of the above a. b. c. d. e. 4-2 In a linear regression equation of the form Y = a + bX, the slope parameter b shows X / Y. Y / X. Y / b. X / b. none of the above a. b. c. d. 4-3 In a linear regression equation of the form Y = a + bX, the intercept parameter a shows the value of X when Y is zero. the value of Y when X is zero. the amount that Y changes when X changes by one unit. the amount that X changes when Y changes by one unit. 4-4 a. b. c. d. a. b. c. d. e. In a regression equation, the ______ captures the effects of factors that might influence the dependent variable but aren't used as explanatory variables. intercept slope parameter R-square random error term 4-5 The sample regression line shows the actual (or true) relation between the dependent and independent variables. is used to estimate the population regression line. connects the data points in a sample. is estimated by the population regression line. maximizes the sum of the squared differences between the data points in a sample and the sample regression line. a. b. c. d. 4-7 The method of least squares can be used to estimate the explanatory variables in a linear regression equation. can be used to estimate the slope parameters of a linear equation. minimizes the distance between the population regression line and the sample regression line. all of the above a. 4-8 In a linear regression equation Y = a + bX, the fitted or predicted value of Y is the value of Y obtained by substituting specific values of X into the sample regression equation. Chapter 4: BASIC ESTIMATION TECHNIQUES b. c. d. e. the value of X associated with a particular value of Y. the value of X that the regression equation predicts. the values of the parameters predicted by the estimators. the value of Y associated with a particular value of X in the sample. a. b. c. d. 4-9 A parameter estimate is said to be statistically significant if there is sufficient evidence that the sample regression equals the population regression. parameter estimated from the sample equals the true value of the parameter. value of the t-ratio equals the critical value. true value of the parameter does not equal zero. a. b. c. d. 4-11 The critical value of t is the value that a t-statistic must exceed in order to reject the hypothesis that the true value of a parameter equals zero. accept the hypothesis that the estimated value of parameter equals the true value. reject the hypothesis that the estimated value of the parameter equals the true value. reject the hypothesis that the estimated value of the parameter exceeds the true value. b. c. b. c. 4-13 In the linear model Y =a +bX +cZ, a test of the hypothesis that parameter c equals zero is a. an F-test. 2 an R -test. a zero-statistic. a t-test. a Z-test. 4-14 If an analyst believes that more than one explanatory variable explains the variation in the dependent variable, what model should be used? a. a simple linear regression model b. a multiple regression model c. a nonlinear regression model d. a log-linear model 4-16 The linear regression equation, Y = a + bX, was estimated. The following computer printout was obtained: DEPENDENT VARIABLE:Y OBSERVATIONS: 18 b. c. d. RSQUARE 0.3066 FRATIO 7.076 PVALUE ON F 0.0171 VARIABLE PARAMETER ESTIMATE STANDARD ERROR TRATIO PVALUE INTERCEPT 15.48 5.09 3.04 0.0008 X 21.36 8.03 2.66 0.0171 Given the above information, the parameter estimate of b indicates a. X increases by 8.03 units when Y increases by one unit. X decreases by 21.36 units when Y increases by one unit. Y decreases by 2.66 units when X increases by one unit. a 10-unit decrease in X results in a 213.6 unit increase in Y. Chapter 4: BASIC ESTIMATION TECHNIQUES 4-17 The linear regression equation, Y = a + bX, was estimated. The following computer printout was obtained: DEPENDENT VARIABLE: OBSERVATIONS: Y 18 RSQUARE 0.3066 FRATIO 7.076 PVALUE ON F 0.0171 VARIABLE PARAMETER ESTIMATE STANDARD ERROR TRATIO PVALUE INTERCEPT 15.48 5.09 3.04 0.0008 X 21.36 8.03 2.66 0.0171 Given the above information, what is the critical value of t at the 1% level of significance? a. b. c. d. 1.746 2.120 2.878 2.921 4-18 The linear regression equation, Y = a + bX, was estimated. The following computer printout was obtained: DEPENDENT VARIABLE: OBSERVATIONS: Y 18 RSQUARE 0.3066 FRATIO 7.076 PVALUE ON F 0.0171 VARIABLE PARAMETER ESTIMATE STANDARD ERROR TRATIO PVALUE INTERCEPT 15.48 5.09 3.04 0.0008 X 21.36 8.03 2.66 0.0171 Given the above information, which of the following statements is correct at the 1% level of significance? a. Both a and b are statistically significant. b. Neither a nor b is statistically significant. c. a is statistically significant, but b is not. d. b is statistically significant, but a is not. 4-19 The linear regression equation, Y = a + bX, was estimated. The following computer printout was obtained: Chapter 4: BASIC ESTIMATION TECHNIQUES DEPENDENT VARIABLE: OBSERVATIONS: a. b. c. d. RSQUARE 0.3066 FRATIO 7.076 PVALUE ON F 0.0171 VARIABLE PARAMETER ESTIMATE STANDARD ERROR TRATIO PVALUE INTERCEPT 15.48 5.09 3.04 0.0008 X 21.36 8.03 2.66 0.0171 Given the above information, the value of the R 2 statistic indicates that 0.3066% of the total variation in Y is explained by the regression equation. 0.3066% of the total variation in X is explained by the regression equation. 30.66% of the total variation in Y is explained by the regression equation. 30.66% of the total variation in X is explained by the regression equation. 4-21 The linear regression equation, Y = a + bX, was estimated. The following computer printout was obtained: DEPENDENT VARIABLE: OBSERVATIONS: a. b. c. d. Y 18 Y 18 RSQUARE 0.3066 FRATIO 7.076 PVALUE ON F 0.0171 VARIABLE PARAMETER ESTIMATE STANDARD ERROR TRATIO PVALUE INTERCEPT 15.48 5.09 3.04 0.0008 X 21.36 8.03 2.66 0.0171 Given the above information, if X equals 20, what is the predicted value of Y? 186.42 165.69 186.42 411.72 4-23 A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results: DEPENDENT VARIABLE: OBSERVATIONS: VARIABLE T RSQUARE FRATIO PVALUE ON F 27 0.7793 42.38 0.0001 PARAMETER ESTIMATE STANDARD ERROR TRATIO Chapter 4: BASIC ESTIMATION TECHNIQUES PVALUE 5150.43 INTERCEPT 1740.72 2.96 G 480.92 130.66 3.68 U 211.0 75.0 2.81 0.0068 0.0012 0.0096 Based on the above information, hiring one more guard per week will decrease the losses due to theft at the warehouse by _________ per week. a. b. c. d. $5,150 $211 $130 $480.92 4-24 A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results: DEPENDENT VARIABLE: OBSERVATIONS: T RSQUARE FRATIO PVALUE ON F 27 0.7793 42.38 0.0001 PARAMETER ESTIMATE STANDARD ERROR TRATIO PVALUE 1740.72 2.96 0.0068 VARIABLE 5150.43 INTERCEPT a. b. c. d. G 480.92 130.66 3.68 U 211.0 75.0 2.81 0.0012 0.0096 Based on the above information, if the firm hires 6 guards and the unemployment rate in the county is 10% (U = 10), what is the predicted dollar loss to theft per week? $4,375 per week $5,150 per week $8,300 per week $9,955 per week 4-25 A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results: DEPENDENT VARIABLE: OBSERVATIONS: T RSQUARE FRATIO PVALUE ON F 27 0.7793 42.38 0.0001 Chapter 4: BASIC ESTIMATION TECHNIQUES VARIABLE INTERCEPT PARAMETER ESTIMATE 5150.43 STANDARD ERROR TRATIO PVALUE 1740.72 2.96 0.0068 G 480.92 130.66 3.68 U 211.0 75.0 2.81 0.0012 0.0096 Based on the above information, a one percent increase in the level of unemployment in the county results in an increase in losses due to theft of __________ more losses per week. a. b. c. d. $75 $211 $280 $460 4-29 Suppose you are testing the statistical significance (at the 5% significance level) of a parameter estimate from the estimated regression equation: Y = a + bR + cS + dW b. c. d. which is estimated using a time-series sample containing monthly observations over a 30month time period. The critical value of the appropriate test statistic is a. tcritical = 2.042. tcritical = 2.056. Fcritical = 4.22. Fcritical = 7.76. 4-30 Suppose you are testing the statistical significance (at the 1% significance level) of a parameter estimate from the estimated regression model: M = a + bR + cI a. b. c. d. e. which is estimated using a crosssection data set on 22 firms. appropriate test statistic is tcritical = 2.861. tcritical = 2.845. tcritical = 2.845. Fcritical = 5.93. Fcritical = 19.44. Fill-in-the-Blank Chapter 4: BASIC ESTIMATION TECHNIQUES The critical value of the 4-1F A simple linear regression equation relates G and D as follows: G = a + bD The explanatory variable is _______, and the dependent variable is ________. The slope parameter is ______, and the intercept parameter _______. When D is zero, G equals _______. For each one-unit increase in D, the change in R is ______ units. 4-2F The linear regression equation G = a + bD is estimated using 24 observations on R and W. The least-squares estimate of b is 22.5, and the standard error of the estimate is 8.36. Perform a ttest for statistical significance of b at the 1% level of significance. a. There are _____ degrees of freedom for the t-test. The value of the t-statistic is _________. The critical t-value for the test is _________. The parameter estimate b _________ (is, is not) statistically significant at the 1% level. 4-3F Thirtytwo data points on Y and X are employed to estimate the parameters in the linear relation Y = a + bX. The computer output from the regression analysis is RSQUARE 0.1911 FRATIO 7.0852 PVALUE ON F 0.0124 VARIABLE PARAMETER ESTIMATE STANDARD ERROR TRATIO PVALUE INTERCEPT X 76.25 124.20 34.98 46.66 2.18 2.66 0.0373 0.0124 DEPENDENT VARIABLE: OBSERVATIONS: Y 32 a. The equation of the sample regression line is: Y = __________________________. b. There are ______ degrees of freedom for the t-test. At the 5% level of significance, the critical t-value for the test is ______________. c. At the 5% level of significance, a __________ (is, not) significant, and b ________ (is, is not) significant. d. At the 2% level of significance, the critical t-value for a t-test is ___________. At the 2% level of significance, a _________ (is, is not) significant, and b_________ (is, is not) significant. e. f. If X equals 240, the fitted (or predicted) value of Y is ____________________________. The percentage of the total variation in Y that is NOT explained by the regression is ________. 4-5F Seventy-five data point on H, U, V, and W are employed to estimate the parameters in the linear relation H =a+bU +cV +dW . The computer output from the regression analysis is shown below: Chapter 4: BASIC ESTIMATION TECHNIQUES H R-SQUARE F-RATIO P-VALUE ON F 75 0.8412 125.36 0.0001 VARIABLE PARAMETER ESTIMATE STANDARD ERROR T-RATIO P-VALUE INTERCEPT 945.0 445.25 2.12 0.0373 U 14.26 5.420 -2.63 0.0104 V -4.10 1.65 -2.48 0.0153 W 25.2 10.5 2.40 0.0190 DEPENDENT VARIABLE: OBSERVATIONS: a. The estimated sample regression line is _________________________________. b. At the 2% level of significance, a _________ (is, is NOT) significant, b _________ (is, is NOT) significant, c_________ (is, is NOT) significant, and d _________ (is, is NOT) significant. c. At the 4% level of significance, a __________ (is, is not) significant, b ________ (is, is not) significant, c________ (is, is not) significant, and ________ (is, is not) significant. d. If U equals 4, V equals 8, and W equals 10, the fitted (or predicted) value of H is ____________. e. The percentage of the total variation in H explained by the regression is ________ percent. Chapter 4: BASIC ESTIMATION TECHNIQUES d