Question

(1 point) The Capital Asset Price Model (CAPM) is a financial model that attempts to predict the rate of return on a financial instrument such as a common stock, in such a way that it is linearly related to the rate of return on the overal market. Specifically, RStockAd Bo+ PRMarket + e You are to study the relationship between the two variables and estimate the above model: 1,2,, 59 RStock Ad-rate of return on Stock A for month i, i RMarket. -market rate of return for month i, i 1,2, ,59 Pr represent's the stocks 'beta' value, or its systematic risk. It measure's the stocks volatility related to the market volatility. Po represents the risk-free interest rate. The data in the Minitab File contains the data on the rate of return of a large energy company which will be referred to Gas and the corresponding rate of return on the Toronto Composite Index (TSE) for 59 randomly selected months. as Acme Oil and Therefore RAcme represents the monthly rate of return for a common share of Acme Oil and Gas stock; RrsEJ represents the monthly rate of return (increase or decrease) of the TSE Index for the same month, month i. The first column in this data file contains the monthly rate of return on Acme Oil and gas stock; the second column contains the monthly rate of return on the TSE index for the same month. (a) Use MINITAB to estimate this model. Use four-decimals in each of your least-squares estimatesyour answer RTSE RAcme + (b) Find the coefficient of determination. Expresses as a percentage, and use two decimal places in your answer. C1 C2 AcmeRofReturn TSERofReturn 0.008850 1 -0.023314 2 0.035088 0.041661 3 0.016949 0.027904 0.043103 0.054967 0.126722 0.069449 6 -0.053790 -0.015124 7 0.108527 0.029879 8 0.076923 0.007837 0.017677 -0.052583 10 0.131514 0.021151 11 0.052632 0.063535 12 -0.066667 0.008640 13 0.109375 0.063966 14 -0.034205 0.040215 15 0.056250 0.060856 16 0.028918 0.143984 0.050605 -0.124138 17 0.027862 0.023622 18 0.000113 19 0.003846 0.055311 20 0.019305 0.061654 -0.041667 21 0.013893 22 -0.047431 -0.009909 23 0.031120 -0.030256 24 -0.050302 0.062824 25 -0.082627 -0.253262 26 0.307159 0.014857 27 0.276667 0.095704 0.031332 28 EOf8a7e6b-2e32-357d-83f6-6ae77994539d C2 C1 AcmeRofReturn TSERofReturn 0.095704 0.031332 28 0.021373 -0.101266 29 0.021904 -0.084507 30 0.036201 0.107692 31 0.066037 -0.100000 32 0.089506 0.043211 33 0.059434 0.124646 34 0.025271 -0.093199 35 0.024004 0.116667 36 0.010021 0.104478 37 -0.015812 38 0.011261 -0.001881 39 -0.008909 0.041137 -0.053933 40 0.035491 -0.021378 41 0.105841 -0.007282 42 0.007942 0.056235 43 0.070970 -0.055556 44 0.035234 0.036765 45 -0.012279 0.179669 46 0.010335 0.146293 47 0.092537 -0.033217 48 0.020263 49 0.034358 0.074823 50 0.092657 -0.083831 51 0.072000 -0.076596 52 -0.044776 -0.092932 53 0.087500 0.096264 0.012734 54 0.041643 -0.083879 55 EC tMinitab Untitled File Edit Data Calc Stat Graph Editor Tools Window Help Assistant A T OV +P c3eb3acf-fc88-3fb7-b91b-3770d736 E Of8a7e6b-2e32-357d-83f6-6ae77994539d C2 C3 C4 C5 C1 AcmeRofReturn TSERofReturn 37 0.104478 0.010021 -0.015812 0.011261 -0.008909 -0.001881 39 40 -0.053933 0.041137 41 -0.021378 0.035491 42 -0.007282 0.105841 43 0.056235 0.007942 44 -0,055556 0,070970 45 0.036765 0.035234 46 0.179669 -0.012279 -0.010335 47 0.146293 48 -0.033217 0.092537 49 0.034358 0.020263 50 0.092657 0.074823 0.072000 -0.083831 -0.076596 -0.044776 0.087500 -0.092932 0.012734 0.096264 -0.083879 0.041643 56 0.031760 -0.153880 57 -0.017194 -0.061872 58 0.200621 0.005052 59 -0.009401 0.063128 60 61 62 63 64 Proj Current Worksheet: 0f8a7e6b-2e32-357d-83f6-6ae77994539d c3eb3acf-fc88-3fb7-b91b-37 552365 The data in the Minitab File contains the data on the rate of return of a large energy company which will be referred to as Acme Oil and Gas and the corresponding rate of return on the Toronto Composite Index (TSE) for 59 randomly selected months Therefore RAcmei represents the monthly rate of return for a common share of Acme Oil and Gas stock; RrSEJ represents the monthly rate of return (increase or decrease) of the TSE Index for the same month, month i. The first column in this data file contains the monthly rate of return on Acme Oil and gas stock; the second column contains the monthly rate of return on the TSE index for the same month. (a) Use MINITAB to estimate this model. Use four-decimals in each of your least-squares estimatesyour answer. RTSE RAcmei + (b) Find the coefficient of determination. Expresses as a percentage, and use two decimal places in your answer. L % (c) In the context of the data, interpret the meaning of the coefficient of determination. A. There is a weak, positive linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE Index. B. There is a strong, positive linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE Index. c. The percentage found above is the percentage of variation in the monthly rate of return of Acme stock that can be explained by its linear dependency with the monthly rate of return of the TSE Index. D. The percentage found above is the percentage of variation in the monthly rate of return of the TSE Index that can be explained by its linear dependency with the monthly rate of return of Acme stock. (d) Find the standard deviation of the prediction/regression, using two decimals in your answer Se (e, i) You wish to test if the data collected supports the statistical model listed above. That is, can the monthly rate of return on Acme stock be expressed as a linear function of the monthly rate of return on the TSE Index? Select the correct statistical hypotheses which you are to test. A. Ho P0 HA : PI0 B. Ho Po0 HA Po0 C. Ho 0 HA Po 0 F. Ho A0 HA : Po 0 G. Ho Ao 0 HA Po> 0 H. Ho : P 0 HA P

Answer 1

Minitab output:

Regression Analysis: AcmeRofReturn versus TSERofReturn

The regression equation is
AcmeRofReturn = 0.0166 + 0.539 TSERofReturn

Predictor Coef SE Coef T P
Constant 0.01665 0.01177 1.41 0.163
TSERofReturn 0.5387 0.1918 2.81 0.007

S = 0.0899527 R-Sq = 12.2% R-Sq(adj) = 10.6%

Analysis of Variance

Source DF SS MS F P
Regression 1 0.063842 0.063842 7.89 0.007
Residual Error 57 0.461215 0.008091
Total 58 0.525057

0.0166 0.5387RTSE,i (a) RAcme,i (b) 2=(0.349)2 100 12.18 % (c) Option C _ 0.09 's (p) (e) (i) Option D. (e) (ii) Feale (e) (ii) P val ue (f) Using Acme stock be expressed 0.063842/0.008091 7.890 0.007 of 5%, this data indicates that the monthly rate of return of as a linear function of the monthly rate of return of an a the TSE index. (g) Lower bound 1-to.025,57 se(B1 0.5387 2.0025 0.1918 where, B0.5387, to.025,57 = 2.0025, se(B) 0.1918 Upper bound 1to025,57 se(1) 0.5387 2.0025 0.1918 (h) Option D 0.155 0.923