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Reading 8 Practice Question #8B- Multiple Regressions (Hypothesis Testing)

Hi,

The question says:

[question removed by moderator]

The Regression equation is

(Analyst following)i = b0 + b1Sizei + b2(D/E) + b3 S&Pi + Ei

Why is the null and alternative hypothesis H0: b3=0 and Ha: b3 not equal 0.

Why isn’t it a 1 tailed test. If we are testing “higher” shouldn’t it be a one sided test?

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AnaValencia wrote:

Hi,

The question says: “Write a multiple regression equation to test whether analyst following is systematically higher for companies included in the S&P 500 index.” The Regression equation is 

(Analyst following)i = b0 + b1Sizei + b2(D/E) + b3 S&Pi + Ei

Why is the null and alternative hypothesis H0: b3=0 and Ha: b3 not equal 0.

Why isn’t it a 1 tailed test. If we are testing “higher” shouldn’t it be a one sided test?

I agree that they’re trying to test the one sided alternative that beta 3 is positive (higher when S&P =1 for included, I’m assuming it’s a dummy variable). (Based on their wording.)

If you want to test the alternative that beta 3 > 0 then the null would be that beta 3 is no greater than zero (less than or equal to, which can be practically written as b3=0).

AnaValencia wrote:
Hi,

The question says: “Write a multiple regression equation to test whether analyst following is systematically higher for companies included in the S&P 500 index.” The Regression equation is

(Analyst following)i = b0 + b1Sizei + b2(D/E) + b3 S&Pi + Ei

Why is the null and alternative hypothesis H0: b3=0 and Ha: b3 not equal 0.

Why isn’t it a 1 tailed test. If we are testing “higher” shouldn’t it be a one sided test?

With all due respect, you need to read the question and answer more carefully.

S&Pi is a dummy variable: 0 if the stock is not in the S&P 500 index, 1 if it is.

The question clearly states that you’re supposed to state the null and alternative hypotheses for a two-sided test.

Simplify the complicated side; don't complify the simplicated side.

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ok i see that the question stated its 2 sided. I just wanted to know why. I understand that S&P is a dummy variable, but what we are testing is the coefficient. Not whether S&P is 0 or 1.

ok i guess

Perhaps question B is simply trying to determine whether inclusion in the S&P 500 matters: good or bad.

Simplify the complicated side; don't complify the simplicated side.

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ok thanks

You’re welcome.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

AnaValencia wrote:

ok i see that the question stated its 2 sided. I just wanted to know why. I understand that S&P is a dummy variable, but what we are testing is the coefficient. Not whether S&P is 0 or 1.

When we want to test a slope statistical significance for a exact value, we use a two-tailed test.

For example: bi = 0, or bi = 2, or bi = -3, etc

When we want to test a slope statistical significance for a comparison value (greater than or lower than), then we use a one-tailed test.

For example: bi > 0, or bi > 2, or bi < -3, etc…

Note that when one-tailed tests are used pay attention if it is an upper-tailed test (when b > 0 for example), or if it is a lower-tailed test (when b < -3 for example).

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S2000magician wrote:

AnaValencia wrote:
Hi,

The question says: “Write a multiple regression equation to test whether analyst following is systematically higher for companies included in the S&P 500 index.” The Regression equation is

(Analyst following)i = b0 + b1Sizei + b2(D/E) + b3 S&Pi + Ei

Why is the null and alternative hypothesis H0: b3=0 and Ha: b3 not equal 0.

Why isn’t it a 1 tailed test. If we are testing “higher” shouldn’t it be a one sided test?

With all due respect, you need to read the question and answer more carefully.

S&Pi is a dummy variable: 0 if the stock is not in the S&P 500 index, 1 if it is.

The question clearly states that you’re supposed to state the null and alternative hypotheses for a two-sided test.

Was this omitted from the original post? I only saw that they wanted to test if “…systematically higher for companies included…”

tickersu wrote:
S2000magician wrote:
AnaValencia wrote:
Hi,

The question says: “Write a multiple regression equation to test whether analyst following is systematically higher for companies included in the S&P 500 index.” The Regression equation is

(Analyst following)i = b0 + b1Sizei + b2(D/E) + b3 S&Pi + Ei

Why is the null and alternative hypothesis H0: b3=0 and Ha: b3 not equal 0.

Why isn’t it a 1 tailed test. If we are testing “higher” shouldn’t it be a one sided test?

With all due respect, you need to read the question and answer more carefully.

S&Pi is a dummy variable: 0 if the stock is not in the S&P 500 index, 1 if it is.

The question clearly states that you’re supposed to state the null and alternative hypotheses for a two-sided test.

Was this omitted from the original post? I only saw that they wanted to test if “…systematically higher for companies included…”

In the preamble to the questions it has this statement: “… the hypothesis is that there is greater demand for analyst coverage for stocks included in the S&P 500 because of the widespread use of the S&P 500 as a benchmark.”

8B itself reads, “State the appropriate null hypothesis and alternative hypothesis in a two-sided test of significance of the dummy variable.”

I don’t know why they asked for a two-sided test for significance, but they did, and that explains their answer being what it was.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/