data analysis using spss
UQ Business School The University of Queensland RBUS 6923 Scientific Method Data Analysis Assignment – Semester 2, 2020 Name: _____________________________ Student Number: _______________________________ Instructions: · The assignment consists of four questions. Please answer all parts of each question. · The data sets available for the various questions are as follows: Question #1 6923.Q1(20-2).xls Question #2 6923.Q2(20-2).xls Question #3 6923.Q3(20-2).xls Question #4 6923.Q4(20-2).xls These data sets can be found on the course blackboard. Question #1 You have collected the following data for Y and for three explanatory variables, X1, X2, and X3. These data can be found in the file ‘6923.Q1(20-2).xls’. Y X1 X2 X3 64.9 4.6 2.95 1,998 35.4 3.4 3.40 1,114 29.6 1.3 4.12 1,942 57.5 3.1 4.43 1,998 71.3 6.9 3.82 2,026 72.4 6.1 4.02 1,853 22.8 6.2 3.32 1,641 61.6 5.4 3.80 1,434 52.9 4.1 3.94 1,513 62.9 5.1 3.85 2,008 64.9 2.9 4.69 1,704 70.5 4.8 3.89 1,525 92.2 3.6 3.53 1,842 88.2 7.2 4.96 1,735 66.9 3.6 3.68 1,639 Required: (a) Estimate the following regression model (using whatever software you would like): e b b b b ˆ ˆ ˆ ˆ ˆ , 3 3 , 2 2 , 1 1 0 i i i i i X X X Y + + + + = (Q1) (b) The theory you are testing suggests the following hypotheses. Do you “accept” or reject the following hypotheses? Clearly explain the logic for your decision. (i) H0: (1 = 0 (ii) H0: (2 = 10 (iii) H0: (3 = 0.100 Question #2 In a 2004 study, Clarkson, Li, and Richardson examine the market valuation of environmental capital expenditure (ECE) investment related to pollution abatement in the pulp and paper industry. They predict that the ECEs of low polluting firms (those that over-comply with existing environmental regulations) will be viewed as an asset by the capital markets (i.e., NPV > 0) while the ECEs of high polluting firms (those that just meet minimal environmental requirements) will be viewed by the capital markets as an expense with no future benefit potential (i.e., NPV = 0). In addition, they predict, that high polluting firms will have unbooked environmental liabilities but that low polluting firms will not (i.e., that the market value of the high polluting firms will be lower, all else held equal). The valuation model they use to test this prediction has the following form: V = β0 + β1 ABV + β2 AE + β3 NECE + β4 NECE * POLLUTE + β5 ECE + β6 ECE*POLLUTE + β7 POLLUTE + υ (Q2) where V = market value of common equity in million dollars, measured three months after the firm’s fiscal year end; ABV = adjusted book value of common equity equal to book value of common equity (BV) minus current period capital expenditure (ECE + NECE), in million dollars; AE = abnormal earnings to common equity, defined as earnings to common equity less an assumed cost of capital based on the CAPM times beginning-of-period book value of common equity, in million dollars NECE = current period non-environmental capital expenditure, in million dollars; ECE = current period environmental capital expenditure, in million dollars; and POLLUTE = an indicator variable set equal to 1 for high polluting firms, and zero otherwise. A modified set of the data used in the study can be found in the file ‘6923.Q2(20-2).xls’. The data in this file are for 28 “pure play” pulp and paper companies that disclosed ECE data over the 12-year period 1989 – 2000. There are a total of 248 firm-year observations in the provided data set. Required: Based on the regression model presented above (equation (Q2)), do the data support the predictions that Clarkson, Li, and Richardson make? In your answer, you should identify the relevant coefficient (or combination of coefficients) to test each of the predictions, state their statistical significance, and finally, explain your conclusion in terms of the significance of the coefficients. Question #3 In a recent study, Artiach and Clarkson (2014) examine the joint impact of conservatism and disclosure on the cost of equity capital. Their study comprises the following three primary hypotheses: H1: Firm level conservatism is inversely related with the cost of equity capital. H2: Firm level disclosure is inversely related with the cost of equity capital. H3: The nature of the relationship between firm level conservatism and the cost of equity capital is conditional on the level of information asymmetry (disclosure). In developing the third hypothesis (H3), they argue that the impact of conservatism on cost of equity capital is likely diminished (weakened) when there is low information asymmetry (high disclosure) because in such a setting, all market participants already have access to considerable public information and thereby the role of conservative accounting is largely redundant. A modified subset of the data used in the study can be found in the file ‘6923.Q3(20-2).xls’. The data cover 1,782 firm-years. The measures included in the file are as follows: COEC = the firm’s cost of equity capital; CONSV = the firm’s conservatism measure; and DISCL = the firm’s disclosure measure. In each instance, higher values denote higher values of the measure (e.g., higher cost of equity capital, more conservative, greater disclosure). Required: (a) Present a single regression model involving the measures identified above which can be used to test all three of Artiach and Clarkson’s hypotheses within this single model. For this model, explain which coefficient is the relevant one to test each hypothesis and what its predicted sign is. (b) Using the data identified above, estimate your proposed regression model. Based on your regression output, do the data support the predictions that Artiach and Clarkson make? In your answer, you should explain your conclusions in terms of the statistical significance and plausibility of the coefficients Question #4 This question consists of three parts, Parts 4.1, 4.2, and 4.3. All three parts are to be answered. For this purpose, the file ‘6923.Q4(20-2).xls’ contains 324 time-series observations of the following (by column): · year and month (January 1974 to December 2000) (month 1 is January) (columns A & B) · monthly returns to ten size-ranked portfolios of Australian stocks (columns H – Q) (note – as labeled, Portfolio 1 is comprised of the smallest stocks while Portfolio 10 is comprised of the largest stocks) · returns to the equally-weighted and value-weighted market indices (columns R & S) · the risk-free rate of return (column T) · for columns D, E, F & G, the formulas reveal the calculations These data should be used to answer each of the three parts of this question (Parts 4.1, 4.2, and 4.3) Part 4.1 It is well documented in the Finance literature that average equity returns in January exceed those of other months. Further, the evidence suggests that this so-called January effect differs between portfolios of small stocks and large stocks. Required: (a) Using the regression model presented immediately below, separately estimate the January effect for the portfolio of the smallest stocks (Portfolio 1) and the portfolio of the largest stocks (Portfolio 10). For the regression, use the equal-weighted market return. Rp,t – Rf,t = (1 + (2 Dt + (p ( RM,t – Rf,t ) + (t (Q4.1) where Rp,t = the return to portfolio p in month t; Rf,t = the risk-free rate of return for month t; RM,t = the return to the market portfolio in month t; and Dt = 1 for January and 0 otherwise. Note, within the context of this model as specified: (p = the beta of the particular size portfolio, p; (1 = the average incremental abnormal return in non-January; and (2 = the incremental abnormal return in January. (b) Present and estimate a single regression model that allows for a formal statistical test of whether there is a small firm effect in the data, and also whether the January effect differs between portfolios of small stocks and large stocks. Again, use the equal-weighted market return. (i) Based upon your regression output, is there a small firm effect? (ii) Based upon your regression output, does the January effect differ between the small stock and large stock portfolios? Hints: The model you develop should be a variant of the model above, modified to incorporate a dummy variable to capture size. Your analysis should be based only on the portfolio of the smallest stocks (Portfolio 1) and the portfolio of the largest stocks (Portfolio 10). To run the regression, the data for these two portfolios should be pooled. Part 4.2 In U.S. studies, it is well documented that average equity returns in January exceed those in other months. Tax-loss selling around the U.S. year-end is offered as an explanation. Interestingly, Australia also has a well-documented January effect, despite having a 30 June financial year-end. Required: (a) Present a dummy-variable regression model that can be used to determine whether Australia exhibits a July effect (to coincide with the Australian tax year) as well as a January effect. In presenting the model, clearly explain all terms and variables. (b) Using this model, estimate the average abnormal return in (i) January, (ii) July, and (iii) the other ten months combined for both the portfolio of small stocks (Portfolio 1) and the portfolio of large stocks (Portfolio 10). Again, use the equal-weighted market return for RM,t in both regressions. Part 4.3 You have a theory that the magnitude of the January effect has changed since the October 1987 stock market crash. You have decided to test this theory using raw returns for the value-weighted market index. In order to remove any potential confounding effects of the crash, you have decided to delete the data for the year 1987 from your sample. Thus, you are interested in two periods: (1) January 1974 through December 1986 (Period 1) and (2) January 1988 through December 2000 (Period 2). Required: (a) Use a single regression model incorporating dummy variables to estimate: (i) the average January return in Period 1 (ii) the average January return in Period 2 (iii) the average return in non-January months during Period 1 (iv) the average return in non-January months during Period 2 (b) Conduct a statistical test on the following hypotheses: (i) there is no difference in January returns between the two sub- periods (ii) there is no difference in non-January returns between the two sub-periods. Note: There are a number of different ways to set up the regression model, all of which