












Find the R^{2} for the least squares regression line that you found.
2. A regression is run using 100 observations to determine the relationship between price and the number of pages in a book. The regression yields this equation:
Price = 1.41 + 1.32(Number of pages)
3. The regression equation for the numbers in the following table is Y = 8 + .5X. What is the standard error of estimate?


















4. Suppose we have run a regression with five observations and we have the following results:
X error 5 1 4 1 1 0 2 ? 0 ?
What are the last two values for the residuals? (Hint: They must sum to zero, and the correlation of the error terms and the independent variables must be zero.)
5. Two researchers were interested in what relationship, if any, existed between a teacher's teaching effectiveness (measured by student evaluations) and his/her research ability (measured by the number of books or articles published over a three year period). Taking a sample of 69, they obtained this result
Teaching Effectiveness = 387.22 + 3.137(Research
Ability)
R2 = .155; tvalue for the regression coefficient = 3.51
6. A teacher used a series of problems in a class that came from a variety of sources. After each set of problems, the students evaluated it in terms of usefulness, with 1 meaning very helpful and 5 meaning useless. The teacher wondered if the material from a prestigious school was better than the rest. He ran a regression using as the dependent variable the average student rating of the set of problems (remember, higher numbers mean less useful) and as an independent variable whether or not the problems came from the prestigious school (0 if from an ordinary school, 1 if from the prestigious school). Below are his results.
Variable
Coefficient
std error
tstatistic
constant
2.285
.034
67.071
Prestige?
.214
.057
3.780
R^{2} = .212
n > 40
(Comment: This is a problem of comparing whether or not two means are the same. Here it is done with regression. It can also be done without regression using a twosample ttest, a test that some introductory texts explain but which I have not included on this site. The results will be the same regardless of which method is used.)
(Use of a zeroone coding is common when we have an offon situation. Variables with this coding are called dummy variables.)
7. Below are the results from a regression trying to predict the asking price of Cadillacs based on their mileage (measured in thousands of miles). (These data were taken from an issue of the Chicago Tribune a number of years ago.)
R Square 
.603 

Adjusted R Square 
.591 



Variable 
Regression Coefficient 
Std. Error 

Significance 
Constant 
26303.415 
1928.098 
13.642 
.000 
miles 
226.465 
32.478 
6.973 
.000 
a) How successful is our attempt to explain the prices of
these cars? (Hint: Use R Square.)
b) If we have a Caddy that has 10,000 miles on it, what
would we predict for its price?
c) The level of significance for miles .000. What is the
hypothesis being tested?
d) There is a problem with the regression. Miles and age
tend to go together, with older cars having more miles.
Perhaps we are capturing some of the effects of age when we
include only miles. How do you think we could fix this
problem?
8. For the data below, compute compute the correlation coefficient for X and Y.











