Pearson Correlation Cannot Be Used to Identify Non-Linear Relationships Between Two Variables

Pearson Correlation cannot be used to identify non-linear relationships between two variables.

A) True

B) False

Regression cannot be used to identify non-linear relationships between two variables.

A) True

B) False

Suppose you have a regression model that depicts the relationship between sales in dollars (S) and the price of the product in dollars (P) such that S = 10 - 2P. Which of the following is the correct interpretation of the price coefficient (i.e., -2)?

A) A $1 increase in price will decrease sales by $2.

B) A $1 increase in sales will occur if there is a $2 decrease in price.

C) A 1% increase in price will cause a 2% decrease in sales.

D) A 1% increase in sales will be caused by a 2% decrease in price.

Suppose you have a regression model that depicts the relationship between sales in dollars (S) and the price of the product in dollars (P) such that log(S) = 10 - 2(logP). Which of the following is the correct interpretation of the price coefficient (i.e., -2)?

A) A $1 increase in price will decrease sales by $2.

B) A $1 increase in sales will occur if there is a $2 decrease in price.

C) A 1% increase in price will decrease sales by 2%.

D) A 1% increase in sales will result from a 2% decrease in price.

Situation 8.1:

A chemist employed by a pharmaceutical company has developed a muscle relaxant. She took a sample of 14 people suffering from extreme muscle constriction. She gave each a vial of the liquid drug and recorded the time to relief (measured in seconds)for each. She then estimated a regression model to this data and found the following: Relief = 1283 (3.65) - 25.22Dose (2.92) - 0.86DoseSquared (2.13) where numbers in parentheses are t-statistics for the corresponding variable coefficient.

The chemist ask you to determine if the there is a significant relationship between dose and time to relief. Using a one-tail test, your best answer would be:

A) Given the results provided, dose is significant at .01 level.

B) Given the results provided, dose is significant at the .05 level.

C) Given the results provided, dose is significant at the .10 level.

D) Given the results provided, dose does not significantly affect time to relief.

Suppose the chemist decides to determine if there is a quadratic effect (e.g. DoseSquared). Should the chemist use a one-tail or two-tail test?

A) A one-tail since the effect of increasing the dosage will eventually taper off so expect dose squared to be negative.

B) A one-tail test since the effect of increasing the dosage will be to accelerate time to relief so expect sign of dose squared is positive.

C) A two-tail test since we do not know what effect an increased dosage will have so do not know sign to expect for dose squared.

D) One could select either a one-tail or two-tail test as long as test at alpha = 0.01.

The chemist concludes that there is a quadratic effect (Dose-squared) for the muscle relaxation medication. This conclusion is appropriate using a two-tail test and alpha = .05.

A) True

B) False

A dummy variable is used when:

A) Two variables are collinear.

B) The model is non-linear

C) The variable is categorical or qualitative.

D) The preferred variable is missing and you must use a proxy variable.

You are hired by a major refrigerator manufacturer to estimate the demand for their refrigerators. You use the following independent variables in this effort.

i. / Population (POP), age 21-35, in thousands.
ii. / Housing starts (H), in thousands.
iii. / Refrigerator price index (P).
iv. / Disposable personal income per capita (Y), in thousands of dollars.
v. / Advertising expenditures (A), in thousands of dollars.
vi. / Replacement trend (R), a replacement probability function constructed from prior refrigerator sales, based on a 16-year average refrigerator life, and average age of refrigerators in market area.

Quarterly data for the years 1997 through 2002 were used to run the regression on refrigerator sales (in thousands). The results are described in Tables 1 and 2 below.

TABLE 1: Regression Results
Variable / Coefficient / t-stat
POP / +0.045 / 1.41
H / +0.657 / 3.13
P / -1579.0 / 2.21
Y / +2254.0 / 1.56
A / +67.5 / 2.74
R / +0.756 / 4.85
CONSTANT / -1245.0 / 1.11
R2= .67 / Adjusted R2= .59 / F = 2.75

TABLE 2:Correlation Matrix

Variables / Correlation / Variables / Correlation / Variables / Correlation
POP,H / .844 / H,P / .356 / P,A / .055
POP,Y / .767 / H,Y / .904 / P,R / -.005
POP,R / -.003 / H,A / .015 / Y,A / .805
POP,P / .450 / H,R / .120 / Y,R / .225
POP,A / .674 / P,Y / .856 / A,R / .022

Assuming that a one-tail test is appropriate for all coefficients and a significance level of .05, which of the variables in the model are significant (exclude constant or intercept from consideration)?

A) R,H,A

B) R,H,A,P

C) R,H,A,P,Y

D) R,H,A,P,Y,POP

10.

What problem can be caused by multicollinearity?

A) The inability to isolate the distinct effects of the related independent variables.

B) Smaller than expected p-values leading to misinterpretations.

C) Smaller than expected standard errors leading to wrong conclusions.

D) Significant t-values and a high R-squared.

11.

Which of the following is the best example of the potential issues associated with multicollineary?

A) Adjusted R-squared is less than R-squared.

B) H and R have a low correlation but both have significant coefficients.

C) POP and Y are correlated and both have insignificant coefficients.

12.

Suppose you check on seasonality in the sales of refrigerators by creating the following variables: Q1 = 1 if first quarter, 0 otherwise; Q2 = 1 if second quarter, 0 otherwise; and Q3 = 1 if third quarter, 0 otherwise. The coefficient for Q2 equals +0.5 and is statistically significant and Q4 is the “omitted” category. Interpret Q2.

A) There are, on average, 500 more refrigerators sold in the second quarter, holding constant the other variables.

B) There are, on average, 500 more refrigerators sold in the second quarter than the first quarter, holding constant the other variables.

C) There are, on average, 500 more refrigerators sold in the second quarter than the third quarter, holding constant the other variables.

D) There are, on average, 500 more refrigerators sold in the second quarter than the fourth quarter, holding constant the other variables.