An ardent fan of television game shows has observed that, in general, the more e
ID: 3311453 • Letter: A
Question
An ardent fan of television game shows has observed that, in general, the more educated the contestant, the less money he or she wins. To test her belief, she gathers data about the last eight winners of her
favorite game show. She records their winnings in
dollars and the number of years of education. The
results are as follows.
1. Determine the standard error of estimate and describe what this statistic tells you about the regression line.
2.Determine the coefficient of determination and discuss what its value tells you about the two variables.
3.Calculate the Pearson correlation coefficient. What sign does it have? Why?
4.Conduct a test of the population coefficient of correlation to determine at the 5% significance level whether a negative linear relationship exists between years of education and TV game shows' winnings.
5.Conduct a test of the population slope to determine at the
5% significance level whether a negative linear relationship exists between years of education and TV game shows' winnings.
6.Do the tests r and b1 in the previous two questions provide the same results? Explain?
Contestant Winnings Years of Education 750 400 600 350 800 300 650 400 15 12 16 4 5 6 16 13 14Explanation / Answer
1)
Standard Error=59.3951. This measures how accurate an estimate is.
2)
r^2=0.92. Describes 92% of the variation in dependent variable is accounted for by the independent variable.
3)
r=0.958. This means that there is a perfect positive correlation amongst the two variables. When the value of one variable goes up, the value of other goes up as well.
4)
H0: =0
H1: < 0
t = r*(n-2) / (1-r^2)
t = (0.96) (6) / ( 1- (0.96)^2)
t= 0.96*2.45/ (1-0.9185)
t = 2.352/0.2855
t = 8.24
The critical t with 6 degrees of freedom (.05 significance level) is 0.729. Calculated t exceeds critical t, so reject H0 in favor of H1. It is reasonable that the coefficient is greater than 0
SUMMARY OUTPUT Regression Statistics Multiple R 0.958379767 R Square 0.918491777 Adjusted R Square 0.904907073 Standard Error 59.39509894 Observations 8 ANOVA df SS MS F Significance F Regression 1 238520.8333 238520.8333 67.61220472 0.000174662 Residual 6 21166.66667 3527.777778 Total 7 259687.5 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1735 147.8926037 11.73148594 2.31479E-05 1373.119835 2096.880165 Yrs of Education -89.16666667 10.84401183 -8.222664089 0.000174662 -115.7010077 -62.6323256Related Questions
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