Practice Problems on Correlation & Simple Regression
1. Suppose that, across a sample of stores, the correlation coefficient between beer prices and beer
sales is 0.65.
What does this number indicate?
(a)
There is almost no variability in beer sales that is unexplained by beer price.
(b)
More beer sales tend to go along with lower beer prices.
(c)
As price increases by $1, beer sales decrease by 65%
(d)
All of the above are true.
Answer: (b)
The correlation is negative, so (b) is correct: higher sales go with lower prices (basic
economics also tells us this!)
Option (a) is false because while .65
2
= 42% of the variability in sales is explained by price,
the remainder (58%) is not explained by price.
(we’ll discuss this interpretation of the
squared correlation next week)
Option (c) is a kind of distorted interpretation of the regression slope
, not the correlation
coefficient.
2. The purpose of a scatterplot is:
3. The standard error of the sample regression slope tells you:
4.
The correlation coefficient describes the _________ between 2 variables.
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5.
R
2
is a measure used to describe the overall fit of the regression line.
Which of the following
statements is/are correct about R
2
?
(a)
In general, the closer the R
2
is to 1, the better the fit of the regression line to the points in the
scatterplot.
(b)
R
2
tells you the proportion of the points in the scatterplot that fall right on the regression line.
(c)
R
2
will always decrease as you add new observations to your regression.
(d)
All of the above are true statements about R
2
.
Answer: (a)
Larger R
2
means a closer fit between the points and the regression line, so (a) is correct
Option (b) is not true (for example, because R
2
could be large even if no points fall right on
the regression line (so long as most of the points are close to the line)
Option (c) is also not true: there is no consistent relation between R
2
and the number of
points; new points can either increase or decrease R
2
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 Spring '09
 Linear Regression, Regression Analysis, Variance, Errors and residuals in statistics, regression line

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