Chapter 10
Correlation and Regression
102
Correlation
1. a. r = the correlation in the sample.
In this context, r is the linear correlation coefficient
computed using the chosen paired (points in Super Bowl, number of new cars sold) values
for the randomly selected years in the sample.
b.
ρ
= the correlation in the population.
In this context,
ρ
is the linear correlation coefficient
computed using all the paired (points in Super Bowl, number of new cars sold) values for
every year there has been a Super Bowl.
c. Since there is no relationship between the number of points scored in a Super Bowl and the
number of new cars sold that year, the estimated value of r is 0.
2. Correlation is the existence of a relationship between two variables – so that knowing the value
of one of the variables allows a researcher to make a reasonable inference about the value of
the other.
Correlation does not imply causality, as there are other factors besides causality that
can be behind a relationship between two variables – e.g., they both could be heavily
influenced by some third variable without having any causeandeffect influence on each other.
3. Correlation is the existence of a relationship between two variables – so that knowing the value
of one of the variables allows a researcher to make a reasonable inference about the value of
the other.
Correlation measures only association and not causality.
If there is an association
between two variables, it may or may not be causeandeffect – and if it is causeandeffect,
there is nothing in the mathematics of correlation analysis to identify which variable is the
cause and which is the effect.
4. Yes; since Table A6 gives the critical values ±0.312, there is sufficient evidence to support a
claim of a linear correlation between the before and after weights.
No; the value of r. while it
indicates a significant linear correlation, does not indicate the diet is effective in reducing
weight.
A correlation simply indicates that the after weight can be predicted from the before
weight (and viceversa), but not whether the after weight was generally larger or smaller (or
even the same) compared to the before weight.
5. a. From Table A6 for n = 62 [closest entry is n=60], C.V. = ±0.254.
Therefore r = 0.758
indicates a significant (positive) linear correlation.
Yes; there is sufficient evidence to
support the claim that there is a linear correlation between the weight of discarded garbage
and the household size.
b. The proportion of the variation in household size that can be explained by the linear
relationship between household size and weight of discarded garbage is r
2
= (0.758)
2
=
0.575, or 57.5%.
6. a. From Table A6 for n = 8, C.V. = ±0.707.
Therefore r = 0.693 indicates a significant
(positive) linear correlation.
Yes; there is sufficient evidence to support the claim that there
is a linear correlation between the heights of mothers and the heights of their daughters.
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 Spring '11
 Dr.Kalluri
 Correlation, Correlation Coefficient, Least Squares, Regression Analysis, Correlation and dependence, σx, Σy, C. Ho

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