Report Statistic IBM

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Fortuna Shanadra – 34414002 Karen Christabel – 34414024

Paulivia Dewi – 34414027 Alvin Kristanto – 34414034

Alamsyah - 34414061

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1. Hypothesis Testing: One-Sample Single Mean with Population Standard

Deviation Unknown

The Medium B class batch 2014 students of International Business Management at Petra Christian University report the mean cost to pay car gasoline in one month is more than IDR 800 thousand rupiahs. Several students say this estimation is too low. To investigate, a random sample of 15 students were conducted. The sample information is reported below.

At the 0.05 significance level, is it reasonable to conclude that the mean cost to pay car gasoline is more than IDR 800 thousand rupiahs?

We will use the six-step hypothesis testing procedure. Step 1: State the null hypothesis and the alternate hypothesis. H0: μ ≤ IDR 800,000 H1: μ > IDR 800,000 Step 2: Select the level of significance. α = 0.05 Step 3: Select the test statistic.

𝑡 = �̅�− 𝜇𝑠

√𝑛

Step 4: Formulate the decision rule.

IDR 1,000,000 1,150,000 800,000

750,000 900,000 800,000

600,000 700,000 1,000,000

600,000 1,200,000 700,000

1,200,000 1,000,000 600,000

Solution

0 1.761

If t-test result < critical value (1.761),

then fail to reject H0 or accept H0.

If t-test result > critical value (1.761),

then reject H0 or accept H1.

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Y X1 X2 X3 X4

Company Year Stock Return Operating Profit Margin Market to Book Value Firm Size Debt Equity Ratio

PT. Astro Agro Lestari Tbk 2010 0.15 33.91% 5.72 15.99 17.90%

2011 -0.17 29.66% 4.20 16.14 21.10%

2012 -0.09 30.48% 3.31 16.33 32.61%

2013 0.27 20.55% 3.85 16.52 46.27%

2014 -0.03 22.63% 3.23 16.74 56.78%

PT. Sampoerna Agro Tbk 2010 0.18 28.37% 2.78 14.87 17%

2011 -0.06 23.83% 5.97 15.04 17.40%

2012 -0.18 16.29% 1.76 15.24 35.40%

2013 -0.17 9.23% 1.42 15.32 48.30%

2014 0.05 17.67% 1.33 15.51 56.30%

PT. Sinar Mas Agro Resources and Technology Tbk 2010 0.96 8.23% 2.46 16.34 114.00%

2011 0.28 7.80% 2.51 16.50 100.69%

2012 0.02 11.85% 2.10 16.60 81.75%

2013 0.20 8.14% 3.48 16.73 183.44%

2014 0.03 6.59% 2.93 16.87 167.97%

PT. PP London Sumatra Indonesia Tbk 2010 0.54 38.96% 19.25 15.53 22.12%

2011 -0.82 42.76% 2.63 15.73 16.31%

2012 0.02 31.44% 2.50 15.84 20.26%

2013 -0.16 24.81% 1.99 15.89 20.58%

2014 -0.02 26.25% 1.79 15.97 19.90%

PT. Gozco Plantations 2010 0.00 35.38% 4.3 14.56 73.94%

2011 0.00 33.91% 2.55 14.86 88.96%

2012 0.02 23.94% 2 14.97 99.20%

2013 -0.07 -21.53% 1.1 14.98 112.94%

2014 0.00 11.39% 1.35 14.99 107.57%

PT. Salim Ivomas Pratama Tbk 2010 0.00 23.60% 0.00 16.86 116.0%

2011 0.00 24.90% 1.20 17.05 68.0%

2012 0.00 17.70% 1.13 17.10 65.0%

2013 -0.32 13.30% 0.75 17.15 74.0%

2014 -0.10 16.30% 0.65 17.25 84.0%

Step 5: Make a decision.

𝑡 = �̅�− 𝜇𝑠

√𝑛= 𝐼𝐷𝑅 866,666.667−𝐼𝐷𝑅 800,000

𝐼𝐷𝑅 215,196.477√15

= 1.199

Step 6: Interpret the result. It is reasonable to conclude that the mean cost to pay car gasoline is more than IDR 800 thousand rupiahs.

2. Multiple Regression Analysis: Agriculture Industry

0 1.761

1.1199

The t-test result (1.199) < critical value (1.761), then fail to reject H0 or accept H0.

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SUMMARY OUTPUT

Regression Statistics

Multiple R 0.560427542

R Square 0.3140

7903

Adjusted R Square

0.204331675

Standard Error

0.255628009

Observations 30

ANOVA

df SS MS F Significance F

Regression 4 0.748034703

0.187008676

2.861836895

0.044250618

Residual 25 1.6336

4198 0.065345679

Total 29 2.381676682

Coeffici

ents Standard Error t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-0.427386686

0.974027482

-0.438782985

0.664587588

-2.433433837

1.578660465

-2.433433837

1.578660465

X Variable 1

-0.486919254

0.49725454

-0.979215301

0.336855155

-1.5110

3415 0.537195642

-1.5110

3415 0.537195642

X Variable 2

0.046019023

0.015536958

2.961906847

0.006615631

0.014020058

0.078017987

0.014020058

0.078017987

X Variable 3

0.018244903

0.061202483

0.298107231

0.768084858

-0.107803971

0.144293776

-0.107803971

0.144293776

X Variable 4

0.174482075

0.137172832

1.271987116

0.215082976

-0.108030661

0.456994812

-0.108030661

0.456994812

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Analysis 1 From the first table, we can see that R2 or coefficient of determination value is 0.314. It means that the independent variables account for 31.4% of the variation in stock return. The adjusted R2 measures the strength of the relationship between the set of independent variables and dependent variable, which is stock return, and also accounts for the number of variables in the regression equation. 0.204 means that the four variables account for 20.4% of the variance of stock return. Second, to find the regression equation, we can look into the last table. In the last table, we can see the coefficient part. Thus, If the equation is �̂� = 𝑎 + 𝑏𝑋1 + 𝑐𝑋2 +𝑑𝑋3 + 𝑒𝑋4, we can find the �̂�, and also the X1-X4. After that, we can put it on the equation and the new equation become �̂� = −0.427 − 0.487𝑏 + 0.046𝑐 +0.018𝑑 + 0.174𝑒. After we get the equation, the interpretation of this equation are:

1. An increase of 1,000 in the value of stock return is followed by the decrease in OPM for -0.487, increase in Market to Book Value for 0.046, increase in firm size 0.018, and last is an increase in debt equity ratio for 0.174.

2. Market to book value, firm size, and debt equity to ratio are positively related with stock return, while operating profit margin is inversely negative toward stock return.

Next step is that we have to conduct the global hypothesis test, in order to check if any of the regression coefficients are different from 0. We use the .05 significance level. 𝒀 = −𝟎. 𝟒𝟐𝟕 − 𝟎. 𝟒𝟖𝟕𝑿𝟏 + 𝟎. 𝟎𝟒𝟔𝑿𝟐 + 𝟎. 𝟎𝟏𝟖𝑿𝟑 + 𝟎. 𝟏𝟕𝟒𝑿𝟒 Step 1 State the null hypothesis and the alternate hypothesis Ho: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 0 H1: Not all of the 𝛽s are 0 Step 2 Select the level of significance 𝛼 = 0.05 Step 3 Determine the test statistic F-test statistic

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Step 4 Formulate a decision rule

F critical value > F test reject Ho F critical value < F test failed to reject Ho Numerator = k = 4 De-numerator = n-(k+1) = 30-(4+1) = 25 F critical value with 0.05 significant level = 2.76 Step 5 Make the decision F test = 2.862 F test > F critical value Reject Ho Step 6 Interpret the result With significant level of 0.05, we can conclude that one of the regression coefficients is not equal to zero. That is why some variables must not be included in the equation. That’s we need to do a t-test to evaluate individual regression coefficient. T-Test Individual Analysis

X1 Step 1 State the null hypothesis and the alternate hypothesis Ho: 𝛽1 = 0 H1: 𝛽1 ≠ 0 Step 2 Select the level of significance 𝛼 = 0.05

2.76

Reject Ho

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Step 3 Determine the test statistic T-test statistic Step 4 Formulate a decision rule

T critical value > T test or T test < T critical value reject Ho df = 25 T critical value with 0.05 significant level = 2.060 Step 5 Make the decision T test = -0.979215301 T test < T critical value Accept Ho Step 6 Interpret the result Since the result is accepting Ho, it means that independent variable 1 is zero.

X2 Step 1 State the null hypothesis and the alternate hypothesis Ho: 𝛽2 = 0 H1: 𝛽2 ≠ 0 Step 2 Select the level of significance 𝛼 = 0.05 Step 3 Determine the test statistic T-test statistic

-2.060

Reject Ho Reject Ho

2.060

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T critical value > T test or T test < T critical value reject Ho df = 25 T critical value with 0.05 significant level = 2.060 Step 5 Make the decision T test = 2.961906847

T test > T critical value Reject Ho Step 6 Interpret the result Since the result is accepting Ho, it means that independent variable 2 is not zero.


-2.060

Reject Ho Reject Ho

2.060

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T critical value > T test or T test < T critical value reject Ho df = 25 T critical value with 0.05 significant level = 2.060 Step 5 Make the decision T test = 0.298107231 T test < T critical value Accept Ho Step 6 Interpret the result Since the result is accepting Ho, it means that independent variable 3 is zero.


-2.060

Reject Ho Reject Ho

2.060

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T critical value > T test or T test < T critical value reject Ho df = 25 T critical value with 0.05 significant level = 2.060 Step 5 Make the decision T test = 1.271987116 T test < T critical value Accept Ho Step 6 Interpret the result Since the result is accepting Ho, it means that independent variable 4 is zero. P-value Analysis From the multiple regression table, we can see that the p-value from the calculation is 0.044. This number less than the critical value which is 0.05. We can conclude then that we reject Ho and that there is one of the coefficient which is not equal to zero. We then see the p-value for each independent variable. The p-value for X1, X3 and X4, which are the operating profit margin, the firm size and the debt to equity ratio, are bigger than the critical value. Which means that these three variable are not significant to stock return. However, p-value for X2, the market to book value, is smaller than the critical value, which means that it is significant and we need to remove the other variable which are not significant. First, we remove the first variable, which is the operating profit margin.

-2.060

Reject Ho Reject Ho

2.060

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SUMMARY OUTPUT



R Square 0.287770871

Adjusted R Square

0.205590587

Standard Error

0.255425701

Observations 30

ANOVA



7174 0.22

8459 3.501702077

0.029484705

Residual 26 1.69629

9508 0.06

5242

Total 29 2.38167

6682

Coeffici

ents Standard Error

t Stat P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-0.503853429

0.970123744

-0.51937

0.607896036

-2.497971343

1.490264485

-2.497971343

1.490264485

X Variable 1

0.041410064

0.014795145

2.798895

0.009533965

0.010998207

0.07182192

0.010998207

0.07182192

X Variable 2

0.014434765

0.061030332

0.236518

0.814884303

-0.111014879

0.139884409

-0.111014879

0.139884409

X Variable 3

0.251335203

0.112412452

2.235831

0.034163813

0.020268099

0.482402306

0.020268099

0.482402306

We can see that there is still some p-value which is bigger than the critical value. So we remove the next variable.

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SUMMARY OUTPUT



R Square 0.286238464

Adjusted R Square

0.233367239

Standard Error

0.250920469

Observations 30

ANOVA



0.340863737

5.413879932

0.010543078

Residual 27 1.699949208

0.062961082

Total 29 2.381676682

Coeffici


P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-0.275768264

0.103852663

-2.655379797

0.013126633

-0.488856328

-0.0626

802

-0.488856328

-0.0626

802

X Variable 1

0.04095218

0.014409225

2.842080637

0.008430399

0.011386892

0.070517467

0.011386892

0.070517467

X Variable 2

0.257381311

0.107536511

2.393431866

0.023907791

0.036734617

0.478028006

0.036734617

0.478028006

We can see when we remove the 3rd variable, which is the firm size. There is still p-value which is bigger than the critical value. So we need to remove the last value which is not significant, the debt equity ratio.

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SUMMARY OUTPUT



R Square 0.134801632

Adjusted R Square

0.10390169

Standard Error

0.271281534

Observations 30

ANOVA



0.321053904

4.362520592

0.045949814

Residual 28 2.060622779

0.073593671

Total 29 2.381676682

Coeffici


P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-0.076118799

0.066884554

-1.138062446

0.264739057

-0.213125597

0.060887999

-0.213125597

0.060887999

X Variable 1

0.031214126

0.014944536

2.088664787

0.045949814

0.000601632

0.06182662

0.000601632

0.06182662

So after we left the market to book value variable only, the significant value is the same. R2 Analysis After we remove all the insignificant variable, we can see that the R2 declined significantly, while when we leave 2 variables behind, the R2 was not declining as much as when we leave 1 variable only. It means that it is okay to use 2 variables because it leads to a better result, since the R2 is closer to 1.

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Report Statistic IBM