Linear Regression

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Show your work for each problem.

1.
What does the slope in a regression line represent?
1. a)The average of all y values
2. b)The number of data points
3. c)How much y changes for each unit increase in x
4. d)The value of y when x = 0
2.
In the regression line , what is the y-intercept?
1. a)10
2. b)3
3. c)13
4. d)30
3.
Using , what is the predicted value of when ?
4.
If a regression line has slope and passes through the point , what is the y-intercept?
5.
A study finds that predicts test scores () based on study hours (). What does the 5 mean?
1. a)The base score with no studying
2. b)Each additional hour of study adds 5 points
3. c)The maximum possible score
4. d)The number of students in the study
6.
Using , predict when .
7.
What is a residual in linear regression?
1. a)The difference between actual and predicted values
2. b)The y-intercept of the line
3. c)The slope of the regression line
4. d)The average of all x values
8.
Find the y-intercept of a regression line with slope that passes through .
9.
The actual value is and the predicted value is . What is the residual?
10.
Given , , and slope , find the y-intercept.
11.
Why should you be cautious about using regression to predict values far outside your data range?
1. a)The y-intercept is undefined outside the range
2. b)The calculations become too difficult
3. c)The slope might change outside the data range
4. d)The relationship may not hold beyond the observed data
12.
Given data: . Find the slope of the regression line.
13.
A regression line is . If , what is the predicted ?
14.
If the sum of squared residuals for a line is minimized, what does this mean?
1. a)The line passes through all points
2. b)All residuals are zero
3. c)This is the line of best fit
4. d)The slope is zero
15.
For the data with slope , find the complete regression equation.
16.
Which of these best describes the purpose of the line of best fit?
1. a)To show the general trend in the data
2. b)To connect the first and last points
3. c)To pass through every data point
4. d)To maximize the distance from points