FLIP!!!
Predictor variable s
- Constant (y intercept) or the predicted value of Y when x=0
- Explanatory variables
B (unstandardized coefficients)
- Called unstandardized coefficients because they are measured in natural units so difficult to compare them due to their different scales
- They predict the dependent variable from the independent variable (using the regression equation)
- Provides values b0, b1, b2, b3 and b4 in that order
B
(equation)
- SciencePredicted = 12.325 +389math +-2.010female+.050socst+.335read
- These estimates tell you about the relationship between the independent variables and the dependent variable.
Interpretation
- For every unit increase in math, a .389 unit increase in science is predicted, holding all other variables constant.
Dummy
- Generally, if a dummy is +2 that means the other dummy must be 2 points lower
- -2.010 unit decrease in the predicted
science score, holding all other variables constant. Since female is coded 0/1 (0=male, 1=female) the interpretation can be put more simply.
- For females, the predicted science score would be 2 points lower than for males.
Beta
- Standardised so all on the same scale
- you can compare the magnitude of the coefficients to see which one has more of an effect.
- larger betas are associated with the larger t-values.
- Beta coefficients are obtained by standardizing all
regression variables into z-scores before computing b-coefficients
P-value
- Test the null hypothesis that the coefficient/parameter is 0.
- P-value lower than alpha means you can reject the null hypothesis that it is significantly different to 0
- Example: The coefficient for socst (.05) is not statistically significantly different from 0 because its p-value is definitely larger than 0.05.
General
- When x increases by 1, y increases by % with all other variables held
constant OR all things being equal
- The baseline binary is always the opposite of the figure seen in the parameter
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1. The assumptions necessary for the test to be valid are:
a. The observations constitutes a simple random sample from the
population of interest, and
b. The expected counts are at least 5 for each cell of the table.
2. Hypotheses
- Null hypothesis: There is no association (independence) between
the row variable and column variable.
- Alternative hypothesis: There is an association (dependence)
between the row variable and column variable.
- In the previous example:
-- H0 : Airline and on-time performance are independent.
-- HA : On-time performance depends on airline.
3. Test Statistic: Χ-Square Statistic
4. P-Value for χ-sqaure test is P(χ^2 - X^2),
df = (r-1)(c-1)
P(χ^2 > test statistic) =
1 - pchisq(testStat, degrees freedom)
5. Decision:
• Rejectt* H0 if the P-value ≤ α.
• Faill* to reject H0 if the P−value > α.
- In our airplane example, P − value
< 0.0001 so we rejectt* the null hypothesis.
6. Conclusion:
- If H0 is rejected then there is a dependence between the row variable and the column variable.
- If H0 is not rejected then there is no association.
- In our airplane example, we reject the null hypothesis. Thus we conclude that on-time status depends on airline.