BUSAN205 Check Your Understanding Topic 3.1
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BUSAN205
Check Your Understanding Topic 3.1
1. For each of the following statements, state whether you agree or disagree with them. Provide your reasoning. You may provide diagrams or algebra or worked examples in your answer if needed.
a) If the regression equation explains nothing, the sum of squared errors (SSE) is zero, thus R2 = 0.
b) In the regression model, the t-statistic is calculated by dividing the slope by the standard deviation of the explanatory variable
c) The principle or the method of least squares is to choose 
and 
in such a manner that for a given set of data, the sum of the residuals is as small as possible.
2. Data is collected on the number of building permits issued each month and the mortgage interest rate in that particular month. Following is an EXCEL output of the regression of BP on Int (where BP is number of building permits issued and Int is the interest rate at the time the building permit is issued. Use this output when answering the following questions.
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
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R Square |
A |
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Adjusted R Square |
0.917 |
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Standard Error |
63.385 |
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Observations |
12 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
492710.6 |
492710.6 |
122.635 |
0.000 |
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Residual |
10 |
40177.09 |
4017.709 |
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Total |
11 |
532887.7 |
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Coefficients |
andard Erro |
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P-value |
Lower 95% |
Upper 95% |
Lower 99.0% |
Upper 99.0% |
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Intercept |
2084.028 |
118.707 |
17.556 |
0.000 |
1819.531 |
2348.524 |
1707.813 |
2460.242 |
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Int |
B |
7.821 |
-11.074 |
0.000 |
-104.036 |
-69.184 |
-111.397 |
-61.823 |
i) Unfortunately, they are two values missing from the table (they are the letters A and B in bold). Calculate the missing values A and B.
ii) State the equation showing that building permits are a function of the interest rate. Give a brief interpretation of the equation. Is this result as you expected?
iii) Test whether there is a relationship between number of building permits issued and interest ret and hence whether interest rate should be included in the regression model to explain number of building permits issued.
iv) It is believed that the higher the interest rate, the few the number of building permits issued. Is the slope coefficient consistent with this hypothesis? Briefly justify your
answer.
v) Use the information from the ANOVA table to test ifR2=0. Briefly explain whether this is the same as testing the coefficient on interest rate equals to zero or not.
vi) What is the 95% confidence interval for the coefficient on Int? What is a 99% confidence interval. Why do they differ?
2022-04-08