Business Smarts - Sample Module for Statistics II

Scenario I
A certified public accountant (CPA) was contracted to analyze the cost data of a manufacturing firm. The firm provided the CPA 60 months of monthly total costs and monthly total production and asked the CPA to construct a regression line. The CPA chose total production, in thousands of coopers, as the independent variable (X) and total cost, in thousands of dollars, as the dependent variable (Y).

ΣX = 156 ΣY = 9,648 ΣX² = 6,864 ΣY² = 1,828,620 ΣX*Y = 324,758 n = 60.
SS_XX = 6,864 - 156²/60 = 6,458.40.
SS_YY = 1,828,620 - 9,648²/60 = 277,221.60.
SS_XY = 324,758 - 156*9648/60 = 299,673.20.

1) What is the slope of the regression line?

 a)  46.4.

 b)  1.1.

 c)  44.6.

 d)  42.9.

 e)  None of the above.

2) What is the intercept of the regression line?

 a)  19.2.

 b)  281.0.

 c)  39.6.

 d)  36.9.

 e)  None of the above.

3) Write the regression line.

 a)  X = 39.640 + 46.400 * Y.

 b)  Y = 39.640 + 46.400 * X.

 c)  Y = 39.640 - 46.400 * X.

 d)  Y = 46.400 + 39.640 * X.

 e)  None of the above.

4) Interpret the slope.

 a)  The marginal cost of each cooper is $46.40.

 b)  The marginal cost of each widget is $46.40.

 c)  The marginal cost of each thousand coopers is $46.40.

 d)  The marginal cost of each cooper is $39.64.

 e)  None of the above.

5) Interpret the intercept.

 a)  The fixed cost of the production process is $39.64.

 b)  The marginal cost of the production process is $39,640.

 c)  The fixed cost of the production process is $39,640.

 d)  The fixed cost of the production process is $46,400.

 e)  None of the above.

Scenario II
A college student chose to estimate a consumption function for a statistics assignment on regression analysis. Total monthly incomes, in thousands of dollars, and total monthly consumption expenditures, in thousands of dollars, were obtained on 100 households. The student chose total income as the independent variable (X) and total expenditure as the dependent variable (Y).

ΣX = 56.80 ΣY = 54.50 ΣX² = 2,360.82 ΣY² = 1,808.44 ΣX*Y = 2,219.15 n = 100.
SS_XX = 2,360.82 - 56.80²/100 = 2,360.50.
SS_YY = 1,808.44 - 5.49²/100 = 1,808.14.
SS_XY = 2,219.15 - 5.68*5.49/100 = 2,216.03.

6) What is the slope of the regression line?

 a)  0.158.

 b)  -0.939.

 c)  1.223.

 d)  0.939.

 e)  None of the above.

7) What is the intercept of the regression line?

 a)  0.526.

 b)  0.158.

 c)  -0.158.

 d)  0.939.

 e)  None of the above.

8) Write the regression line.

 a)  Y = 0.939 + 0.158 * X.

 b)  Y = -0.158 + 0.939 * X.

 c)  Y = 0.158 + 0.939 * X.

 d)  Y = 0.158 + 0.939 * Z.

 e)  None of the above.

9) Interpret the slope.

 a)  The marginal propensity to save is 0.939.

 b)  The marginal propensity to consume is 0.939.

 c)  The marginal propensity to consume is 0.158.

 d)  The average propensity to consume is 0.939.

 e)  None of the above.

10) Interpret the intercept.

 a)  The monthly autonomous consumption is $158.

 b)  The monthly autonomous consumption is $15,800.

 c)  The monthly autonomous consumption is $939.

 d)  The annual autonomous consumption is $158.

 e)  None of the above.

Scenario III
A human resources manager decides to regress total monthly pay of each of the firm's 75 salespersons against the total monthly sales by that salesperson. The manager chose total sales, in tens of thousands of dollars, as the independent variable (X) and total pay, in thousands of dollars, as the dependent variable (Y).

ΣX = 7,312.5 ΣY = 8,805.0 ΣX² = 824,070.25 ΣY² = 2,482,080 ΣX*Y = 974,652.0 n = 75.
SS_XX = 824,070.25 - 7,312.5²/75 = 111,101.50.
SS_YY = 2,482,080 - 8,805.0²/75 = 1,448,373.0.
SS_XY = 974,652.0 - 7,312.5*8,805.0/75 = 116,164.50.

11) What is the slope of the regression line?

 a)  1.456.

 b)  0.080.

 c)  1.046.

 d)  -1.046.

 e)  None of the above.

12) What is the intercept of the regression line?

 a)  16.457.

 b)  15.075.

 c)  25.253.

 d)  -15.457.

 e)  None of the above.

13) Write the regression line.

 a)  Y = 15.457 + 1.046 * X.

 b)  Y = 1.046 + 15.457 * X.

 c)  Y = 15.457 - 1.046 * X.

 d)  W = 15.457 + 1.046 * X.

 e)  None of the above.

14) Interpret the slope.

 a)  The sales commission rate is $1,046 per $1,000 of sales, or 104.6%.

 b)  The sales commission rate is $1,046 per $10,000 of sales, or 10.46%.

 c)  The sales commission rate is $104.6 per $10,000 of sales, or 1.046%.

 d)  The sales commission rate is $1,046 per $100,000 of sales, or 1.046%.

 e)  None of the above.

15) Interpret the intercept.

 a)  The base pay is $1,046.

 b)  The base pay is $15.457.

 c)  The base commission is $15,457.

 d)  The base pay is $15,457.

 e)  None of the above.

Scenario IV
A financial analyst investigates the relationship between the riskiness of certain securities and their returns. Data on 80 stocks are collected. The analyst chooses risk, in percent, as the independent variable (X) and return, in percent, as the dependent variable (Y).

ΣX = 484.0 ΣY = 740.0 ΣX² = 6,180.0 ΣY² = 15,720.0 ΣX*Y = 9,226.32 n = 40.
SS_XX = 6,180 - 484.0²/40 = 323.60.
SS_YY = 15,720.0 - 740.0²/40 = 2,030.0.
SS_XY = 9,326.32 - 484*740/75 = 372.32.

16) What is the slope of the regression line?

 a)  4.578.

 b)  1.833.

 c)  1.151.

 d)  -1.151.

 e)  None of the above.

17) What is the intercept of the regression line?

 a)  -4.578.

 b)  -9.186.

 c)  4.578.

 d)  2.891.

 e)  None of the above.

18) Write the regression line.

 a)  Y = -4.578 + 1.151 * X.

 b)  Y = 1.151 + 4.578 * X.

 c)  Y = 4.578 + 1.151 / X.

 d)  Y = 4.578 + 1.151 * X.

 e)  None of the above.

19) Interpret the slope.

 a)  The risk premium, the additional return investors need in compensation
       for additional risk, is 4.58%.

 b)  The risk premium, the additional return investors need in compensation
       for additional risk, is 1.15%.

 c)  The risk premium, the additional return investors need in compensation
       for additional risk, is -1.15%.

 d)  The return premium, the additional risk investors need in compensation
       for additional return, is 1.15%.

 e)  None of the above.

20) Interpret the intercept.

 a)  The risk-free rate of return is 4.58%.

 b)  The risk-free rate of return is 1.15%.

 c)  The marginal rate of return is 4.58%.

 d)  The risk-free rate of return is -4.58%.

 e)  None of the above.

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