Statistics
1. In a Physics class, the correlation between the students ’ total scores prior to the final and their
final examination scores is r = 0.6. The pre-exam totals for all students have a mean of 280 and a
standard deviation of 30. Their final exam scores have a mean of 75 and a standard deviation of 8.
The professor ha s lost Julia’ s final exam, but knows that her total before the exam was 300. He
decides to predict her final exam score from her pre -exam total.
a. Find the equation of the least squares regression line.
b. Predict Julia ’ s final exam score
c. Julia doesn ’ t believe that this method accurately predicts how well she did on the final
exam. Argue that her final exam score could have been much higher (or lower) than the
predicted value. Explain your rationale clearly.
2. A survey of the world ’ s nations in 2004 shows a strong positive linear association between the
number of televisions per household in a country and the country’s life expectancy in y ears.
a. Does this mean that watching television in creases life expectancy?
b. Give a lurking variable that may explain this relationship and explain how the lurking
variable affects BOTH of the variables involved.
3. The following is part of a MINITAB printout for a regression of x (alcohol from wine) and y
(HDD -heart disease death rate) for 19 countries:
The regression equation is
HDD = 260.6 – 22.97 alcohol
S = 37.8786 R
2
= 71.0%
a. Find and interpret the correlation coefficient (r)
b. Interpret R
2
.
4. A sample of married couples is taken and the systolic blood pressures of the husbands and wives
are each measured. The correlation between the systolic blood pressure of the husbands and the
systolic blood pressures of the wives is found to be 0.2 7.
a. Does the correlation help answer the question of who has higher systolic blood pressures
– the husbands or the wives? Explain clearly .
b. If all the women in the sample had 3 0 points higher systolic blood pressures , would the
value of the correlation coefficient be higher, lower or the same? Explain clearly and
completely why.
5. The following question must be done using the computer : (data file childfev .mtw on Moodle)
A sample of 654 children was taken and the FEV (Forced expiratory Volume) was measured and
compared to their ages.
a. Perform the least squares regression analysis by printing out the fitted line plot. (Be
careful to choose x and y correctly)
b. From this, state clearly the regression line and state and interpret both the correlation
coefficient (r) and the coefficient of determination (r
2
).
c. Estimate the FEV of a child who is 13 ye ars old. Do you think this estimate would be
fairly accurate? Explain clearly why or why not.
d. Explain clearly why you would not use this model to estimate the FEV of a 24 year old .