In: Statistics and Probability
Suppose the following data were collected relating CEO salary to years of experience and gender. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average male CEOs have higher salaries than female CEOs at the 0.010.01 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."
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Salary | Experience | Male (1 if male, 0 if female) |
---|---|---|
100978.79100978.79 | 1818 | 00 |
134750.31134750.31 | 2020 | 11 |
82777.4482777.44 | 11 | 11 |
101472.37101472.37 | 1919 | 00 |
100000.00100000.00 | 1515 | 00 |
125574.97125574.97 | 2020 | 11 |
74970.6274970.62 | 44 | 11 |
85390.0885390.08 | 88 | 11 |
107504.05107504.05 | 2828 | 00 |
105981.49105981.49 | 2626 | 00 |
97737.9197737.91 | 1010 | 11 |
115000.00115000.00 | 1515 | 11 |
82528.6282528.62 | 33 | 11 |
104295.79104295.79 | 2828 | 00 |
103053.49103053.49 | 2525 | 00 |
105575.83105575.83 | 1212 | 11 |
100000.00100000.00 | 1515 | 00 |
101694.06101694.06 | 1818 | 00 |
85141.2685141.26 | 77 | 11 |
108282.06108282.06 | 3030 | 00
Answer(How to Enter) 2 Points Keypad Selecting a checkbox will replace the entered answer value(s) with the checkbox value. If the checkbox is not selected, the entered answer is used. SALARYi=SALARYi= b0 ++ b1 EXPERIENCEiEXPERIENCEi ++ b2 MALEi+eiMALEi+ei There is not enough evidence |
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.815559299 | |||||||
R Square | 0.66513697 | |||||||
Adjusted R Square | 0.625741319 | |||||||
Standard Error | 8825.378852 | |||||||
Observations | 20 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 2 | 2630022847 | 1315011424 | 16.88351275 | 9.14895E-05 | |||
Residual | 17 | 1324084302 | 77887311.89 | |||||
Total | 19 | 3954107149 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 61314.98396 | 7876.348753 | 7.784696423 | 5.28119E-07 | 44697.34082 | 77932.62711 | 44697.34082 | 77932.62711 |
Experience | 1892.397569 | 331.7717821 | 5.703913568 | 2.58475E-05 | 1192.420302 | 2592.374837 | 1192.420302 | 2592.374837 |
Male (1 if male, 0 if female) | 18705.74434 | 5653.375591 | 3.308774385 | 0.004150715 | 6778.164565 | 30633.32412 | 6778.164565 | 30633.32412 |
P value for male = 0.004 < 0.01
So, it is significant
there is enough evidence to claim that on average male CEOs have higher salaries than female CEOs at the 0.01 level of significance
Equation :
Salary = 61314.98 + 1892.41 * Experience + 18705.74 * Male
Salary difference between male(1) and Female(0)
Difference = 18705.74(1-0) = 18705.74