Question

In: Statistics and Probability

To determine whether the cash bonuses paid by Johnson Financial Group are related to annual pay,...

To determine whether the cash bonuses paid by Johnson Financial Group are related to annual pay, data were gathered for 10 account executives who received such bonuses in 2007.

The data, scatterplot and summary statistics are shown below.

ANNUAL PAY CASH BONUS
$70,723 $11,262
$58,612 $6,313
$104,706 $14,252
$44,025 $4,235
$82,786 $11,884
$116,342 $23,731
$76,861 $7,826
$68,639 $20,818
$137,069 $55,012
$94,524 $34,426

1) Comment on whether each of the following conditions for correlation / linear regression is met
- Quantitative Variables Condition
- Linearity Condition
- Outlier Condition

2) Estimate the linear regression model that relates the response variable (Cash Bonus) to the predictor variable (Annual Pay)
Find the slope of the regression line.  

Find the intercept of the regression line.  

Write the equation of the linear model.

3) Find the value of R2. Interpret its meaning in this context

4) Using the regression equation, estimate the cash bonus for an executive at Johnson Financial earning $82,786 a year.
What is the residual for this estimate? What does it mean?

Solutions

Expert Solution

1. Checking for conditions with scatter plot

Conditions met: Quantitative Variables Condition and Linearity Condition

2. Using Excel, go to Data, select Data Analysis, choose Regression. Put Annual Pay in X input range and Cash Bonus in Y input range.

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.812
R Square 0.659
Adjusted R Square 0.616
Standard Error 9677.023
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 1448230160.971 1448230160.971 15.465 0.004
Residual 8 749158209.929 93644776.241
Total 9 2197388370.900
Coefficients Standard Error t Stat P-value
Intercept -19637.790 10284.742 -1.909 0.093
Annual pay 0.452 0.115 3.933 0.004

Slope = 0.452

Intercept = -19637.79

y = -19637.79 + 0.452x

Cash bonus = -19637.79 + 0.452*Annual pay

3. R-square = 0.659

Thihs means that 65.9% variation in cash bonus is explained by annual pay.

4. Annual pay = $82,786

Estimated Cash bonus = -19637.79 + 0.452*82786 = $17,781.482

Actual cash bonus = $11,884

Residual = 11884-17781.482 = -5897.482

This means estimated value is $5897 more than actual value of cash bonus.

orchestra answered 1 year ago
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