# quant

Henry Hilton, CFA, is undertaking an analysis of the bicycle industry. He hypothesizes that bicycle sales (SALES) are a function of three factors: the population under 20 (POP), the level of disposable income (INCOME), and the number of dollars spent on advertising (ADV). All data are measured in millions of units. Hilton gathers data for the last 20 years and estimates the following equation (standard errors in parentheses): SALES = α + 0.004 POP + 1.031 INCOME + 2.002 ADV (0.005) (0.337) (2.312) The critical t-statistic for a 95% confidence level is 2.120. Which of the independent variables is statistically different from zero at the 95% confidence level? A) ADV only. B) INCOME only. C) INCOME and ADV.

1.031/0.337 = 3.059 2.002/2.312 = 0.8659 >> low B?

t-stat pop= 0.8 t stat income = 3.05 t stat adv = 0.87 B.

Definitely B, even without knowing the critical t it is the only one within the realm of possibility.

Consider the following estimated regression equation, with the standard errors of the slope coefficients as noted: Salesi = 10.0 + 1.25 R&Di + 1.0 ADVi – 2.0 COMPi + 8.0 CAPi where the standard error for the estimated coefficient on R&D is 0.45, the standard error for the estimated coefficient on ADV is 2.2 , the standard error for the estimated coefficient on COMP is 0.63, and the standard error for the estimated coefficient on CAP is 2.5. The equation was estimated over 40 companies. Using a 5% level of significance, which of the estimated coefficients are significantly different from zero? A) R&D, ADV, COMP, and CAP. B) ADV and CAP only. C) R&D, COMP, and CAP only. I’m struggling with these questions as I did for Level 1.

B… trick question?

B

Reject Rules Big T Little P

C

Which of the following statements regarding the results of a regression analysis is FALSE? The: A) slope coefficient in a multiple regression is the value of the dependent variable for a given value of the independent variable. B) slope coefficient in a multiple regression is the change in the dependent variable for a one-unit change in the independent variable, holding all other variables constant. C) slope coefficients in the multiple regression are referred to as partial betas.

Answers b c a Can someone enlighten dumbdigger how to look up 35 degrees of freedom on the t table? I see 30 and 40 df, and the 5% interval equals 2.04 and 2.02 respectfully. Do you simply average the two? It seems like a stretch. Your answer: B was incorrect. The correct answer was C) R&D, COMP, and CAP only. The critical t-values for 40-4-1 = 35 degrees of freedom and a 5% level of significance are ± 2.03. The calculated t-values are: t for R&D = 1.25 / 0.45 = 2.777 t for ADV = 1.0/ 2.2 = 0.455 t for COMP = -2.0 / 0.63 = -3.175 t for CAP = 8.0 / 2.5 = 3.2 Therefore, R&D, COMP, and CAP are statistically significant.

Don’t make it so hard. Multiple SE by 2.1 +/- SE If 0 is in your interval reject. That should be enough for the L2 exam.

A) slope coefficient in a multiple regression is the value of the dependent variable for a given value of the independent variable.

Unless you’re doing the dependent variable In that case sf^2 = SEE^2 ( 1/n + …) What’s that formula again?

since over 40 - approximate to normal so t needs to be > 1.96 t = (x-0) / se R&Di = 1.25-0 / 0.45 = 2.77 yes ADVi = 1-0 / 2.2 = 0.45 no COMPi = 2-0 / 0.63 = 3.17 yes CAP = 8-0 / 2.5 = 3.2 yes C

swaptiongamma, danlieb, my quantitatively inclined friends, I know you remember ;D

DanLieb Wrote: ------------------------------------------------------- > Don’t make it so hard. Multiple SE by 2.1 +/- SE > If 0 is in your interval reject. > > That should be enough for the L2 exam. Excuse me, fail to reject the null hypothesis that the IV predicts the DV

I don’t get this one. Consider the following estimated regression equation, with calculated t-statistics of the estimates as indicated: AUTOt = 10.0 + 1.25 PIt + 1.0 TEENt – 2.0 INSt with a PI calculated t-statstic of 0.45, a TEEN calculated t-statstic of 2.2, and an INS calculated t-statstic of 0.63. The equation was estimated over 40 companies. Using a 5% level of significance, which of the independent variables significantly different from zero? A) PI and INS only. B) PI only. C) TEEN only. Your answer: B was incorrect. The correct answer was C) TEEN only. The critical t-values for 40-3-1 = 36 degrees of freedom and a 5% level of significance are ± 2.028. Therefore, only TEEN is statistically significant.

Ditch: Read carefully? Only Tcalc(Teen) > T(crit)

I think I should change my name to dumbdigger. In any case, I learn from mistakes. So I don’t feel bad posting simple questions on AF. Thanks Dan, read the question too fast and thought this was similar to another one I did where the standard error was present.