Question

A financier whose specialty is investing in movie productions has observed that, in general, movies with "big-name" stars seem to generate more revenue than those movies whose stars are less well known. To examine his belief, he recorded the gross revenue and the payment (in $ millions) given to the two highest-paid performers in each movie for ten recently released movies

Movie Cost of Two highest paid performers    Gross Revenue

1    5.3 48

2 7.2    65

3 1.3    18

4 1.8 20

5 3.5 31

6 2.6 26

7 8.0 73   

8 2.4 23

9 4.5 39

10 6.7    58

a) Determine the standard error of estimate and describe what this statistic tells you about the regression line.

b) Determine the coefficient of determination and discuss what its value tells you about the two variables.

c) Calculate the Pearson correlation coefficient. What sign does it have? Why?

Answer 1

(a) The standard error of the estimate is 2.025.

The Standard Error of Estimate is the measure of the variation of an observation made around the computed regression line. Simply, it is used to check the accuracy of predictions made with the regression line.

(b) The coefficient of determination is 0.991.

99.1% of the variability in the model is explained.

(c) The Pearson correlation coefficient is 0.995.

There is a strong positive relationship between x and y.

	r²	0.991
	r	0.995
	Std. Error	2.025
	n	10
	k	1
	Dep. Var.	of
ANOVA table
Source	SS	df	MS	F	p-value
Regression	3,520.1052	1	3,520.1052	858.70	1.99E-09
Residual	32.7948	8	4.0993
Total	3,552.9000	9
Regression output				confidence interval
variables	coefficients	std. error	t (df=8)	p-value	95% lower	95% upper
Intercept	4.2254
Cost	8.2851	0.2827	29.304	1.99E-09	7.6331	8.9371