ECON 203 Lecture Notes - Lecture 8: List Of Statistical Packages, Statistical Hypothesis Testing, Coefficient Of Determination
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*** Please see p. 2 for Question 2 ***
Question 2 (7 points)
The following Excel output shows the outcome of a linear regression of individuals%u2019 wage per hour (in dollars) on the number of years they attended school (in years).
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.381932619 | |||||||
R Square | 0.145872525 | |||||||
Adjusted R Square | 0.144267022 | |||||||
Standard Error | 4.753758428 | |||||||
Observations | 534 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 2053.22554 | 2053.22554 | 90.8578469 | 5.45998E-20 | |||
Residual | 532 | 12022.25261 | 22.59821919 | |||||
Total | 533 | 14075.47815 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Upper 95.0% | ||
Intercept | -0.745942699 | 1.045403804 | -0.71354504 | 0.475821452 | -2.799566599 | 1.307681201 | 1.307681201 | |
Years of School | 0.750448943 | 0.078729942 | 9.531938255 | 0.000545998 | 0.595789385 | 0.9051085 | 0.9051085 |
Part (a) (1 point)
What is the value of the estimated slope %u201Cb%u201D?
Part (b) (2 points)
Interpret the estimated value of the slope (i.e., explain what the number means in this regression).
Part (c) (1 point)
Is the estimate of the slope statistically significant? Please answer %u201Cyes%u201D or %u201Cno%u201D and explain how you can tell.
Part (d) (2 points)
Explain why we want to be able to reject the null hypothesis H0: %u03B2 = 0.
Part (e) (1 point)
How much of the total variation in wages can be explained by individuals%u2019 education?
1. Write the subsequent demand equation, with Qd as the dependent variable; price, advertising, product development, and rel price as the independent variables.
2. How strong is the relationship between quantity demanded and the set of independent variables? List and explain 2 measures of this strength.
3. Which variable is most important in determining quantity demanded? Why?
Regression Statistics | ||||||||
Multiple R | 0.655864641 | |||||||
R Square | 0.430158427 | |||||||
Adjusted R Square | 0.104534671 | |||||||
Standard Error | 102678.3385 | |||||||
Observations | 12 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 4 | 55709596185 | 13927399046 | 1.321029008 | 0.349980066 | |||
Residual | 7 | 73799888386 | 10542841198 | |||||
Total | 11 | 1.29509E+11 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | 1422378.519 | 1185014.572 | 1.200304665 | 0.269060955 | -1379735.677 | 4224492.715 | -1379735.677 | 4224492.715 |
X Variable 1 | -247037.6649 | 160481.181 | -1.539355975 | 0.167610603 | -626515.3574 | 132440.0276 | -626515.3574 | 132440.0276 |
X Variable 2 | 0.081609431 | 1.398101115 | 0.058371623 | 0.955083996 | -3.22437437 | 3.387593232 | -3.22437437 | 3.387593232 |
X Variable 3 | -1.015253706 | 3.150288749 | -0.322273222 | 0.756657161 | -8.46450288 | 6.433995469 | -8.46450288 | 6.433995469 |
X Variable 4 | 177211.9244 | 145755.2053 | 1.215818838 | 0.263460235 | -167444.3689 | 521868.2176 | -167444.3689 | 521868.2176 |