E-Text Week 5 Team A
E-Text Week 5 Team A
Chapter 12 Review # 1 (a) How does correlation analysis differ from regression analysis? (b) What does a correlation coefficient reveal? (c) State the quick rule for a significant correlation and explain its limitations. (d) What sums are needed to calculate a correlation coefficient? (e) What are the two ways of testing a correlation coefficient for significance?
a) The correlation analysis identifies the relationship between two variables of interest. The regression analysis uses one or more independent variables (x) to predict the value of the dependent variable (y) using a scatter plot to view the relationships ...view middle of the document...
7963 + 0.0343x
b) The df = 33 so the cv is 2.035
c) The value is not zero because the p-value is .0068 < .05.
d) With a 95% confidence level we can say that the slope is between 0.0101 (lower) and 0.0584 (upper).
e) F= t2.8892 = 8.346321 rounded to 8.35
f) The correlation between x and y are low with R2 = 0.202 and the standard error rate is high for y and x at 6.816.
12.50 In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64 large banks. (a) Write the fitted regression equation. (b) State the degrees of freedom for a twotailed test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression.
a. Y = 0.0452X + 6.5763
b. Degrees of Freedom = 63 and Critical Value = 5.291
c. The slope does equal 0, and the p-value is greater than .05 so we are able to accept the bull hypothesis.
d. 95% Confidence Interval.
Upper Limit = 0.056
Lower Limit = 0.034
e. t2 = 8.1832
t2 = 66.961
Yes, it fits.
f. This regression fits well because variation of X can be expianed for over 50% of Y. This means that the majority of the variation is accounted for.
13.30 A researcher used stepwise regression to create regression models to predict BirthRate (births per 1,000) using five predictors: LifeExp (life expectancy in years), InfMort (infant mortality rate), Density (population density per square kilometer), GDPCap (Gross Domestic Product per capita), and Literate (literacy percent). Interpret these results.
Interpretation: The next aspect of this test that stands out is the high value of R^2. This leads me to the conclusion that the slopes of these variables pair well and account for any significant variation. This shows us that there is a strong level of correlation between the dependent variables. Also, the p-values for GDPcap and Literacy are very low. This leads me to believe that literacy levels amount to a lower infant mortality rate and a higher GDP per capital also has a positive impact.
13.32 An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise).
Variable Coefficient t p
Intercept −3,816,521 −29.4 .000
Year 1,948 29.8 .000
YearHire −826 −5.5 .000
Race −2,093 −4.3 .000
Rank −6,438 ...