Ch. 9 Pretest
Correlation & Residuals
Name ______________________________
Period _________
1.
The number of students in a school chorus has increased since the school first
opened 6 years ago.
Find the Linear Regression Equation
# of StuPredicted # Residual a)
Year
dents
of Students Value
0
22
1
26
2
40
3
59
4
78
c) Find the correlation coefficient.
5
83
d) Interpret the correlation coefficient.
b)
Interpret the Regression Equation.
e) Fill in the table above with the predicted # of students (using your regression
equation) and the Residual Values for the years listed.
f) Construct a scatter plot and sketch the
the line of best fit.
g) Construct a Residual Plot using
the table.
h) Based on the residual plot do you think a linear model is a good fit? Why?
2. The weekly sales of an album have decreased since it was first sold at a music store 6
weeks ago.
Week
0
# of
Predicted #
Albums of Albums
Sold
Sold
23
1
21
2
18
3
17
4
19
5
12
Residual
Value
a)
Find the Linear Regression Equation
b)
Interpret the Regression Equation.
c) Find the correlation coefficient.
d) Interpret the correlation coefficient.
e) Fill in the table above with the predicted # of albums sold (using your regression
equation) and the Residual Values for the years listed.
f) Construct a scatter plot and sketch the
the line of best fit.
g) Construct a Residual Plot using
the table.
h) Based on the residual plot do you think a linear model is a good fit? Why?
3. While in high school, Claudia started her own T-shirt printing business. The table
shows the number of T-shirts Claudia has sold each year since starting his business
in 2006.
Year
# of
T-shirts
2006
180
2007
250
2008
50
2009
125
2010
95
2011
145
2012
75
Predicted
# of
T-shirts
Residual
Value
a)
Find the Linear Regression Equation
b)
Interpret the Regression Equation.
c) Find the correlation coefficient.
d) Interpret the correlation coefficient.
e) Fill in the table above with the predicted
# of albums sold (using your regression equation) and the Residual Values for the
years listed.
f) Construct a scatter plot and sketch the
the line of best fit.
g) Construct a Residual Plot using
the table.
h) Based on the residual plot do you think a linear model is a good fit? Why?
4. What is the difference between interpolation and extrapolation?
5. The table shows the population decline of a small town over a seven-year period.
Year
2005
2006
2007
2008
2009
2010
Population
9.4
8.3
8.9
8.0
6.9
6.3
(Thousands)
a. Determine the linear regression equation (with 2005 being year 0)
2011
6.6
b. Interpret the equation in terms of the problem situation.
c. Predict the population of the town in 2014 using your regression equation.
d. Do you think your prediction seems reasonable? Explain.
e. Predict the population of the town in 2090 using your regression equation.
f. Explain whether your prediction is reasonable. Is this interpolation or extrapolation?
g. Predict the population of the town in 2010 using your regression equation. Is this interpolation or extrapolation?
h. Predict the population of the town in 2000 using your regression equation. Is this interpolation or extrapolation?
6. Sketch multiple examples of residual plots that indicate a linear model:
a. may be appropriate for a data set.
b. may not be appropriate for a data set.
7. Explain how to find the residual value and what it represents.
8. Sketch an example of a scatter plot with:
a. positive correlation.
b. negative correlation.
c. no correlation.
9. What correlation coefficients (r-value) are most appropriate (accurate) for a
a. positive correlation?
b. negative correlation?
c. no correlation?
10. Sketch a line of best fit and write a possible linear regression equation for each scatterplot.
a.
b.
c.
d. For each of the three scatterplots above, estimate what you think the correlation coefficient
might be for your regression equation and EXPLAIN your reasoning.
11. Write an equation of the line that goes through the following points:
𝑎. (3, 4) and (0, 5)
b. (−2, 6) and (4, 7)
c. (3, 4) and (5, 8)
12. Graph the following systems of equation, and estimate the solution using the graph:
2
a. 𝑦 = 𝑥 − 4
3
𝑦 = −4
1
b. 𝑦 = − 𝑥 + 2
4
c. 2𝑥 − 𝑦 = 6
𝑥=3
f.
|2𝑥 − 4| = 4
2
𝑦 = −3𝑥 + 1
13. Solve each of the following equations for x:
a. 2𝑥 + 1 = 5𝑥
b. 4𝑥 − 3𝑥 + 9 = 12
d. 5 − 4(2𝑥 + 3) = 3𝑥 − 4
d. 𝑦 = 𝑥 − 1
𝑦 =− 𝑥+4
5
c. 10𝑥 − 1 = 7𝑥 − 3
e.
10 − 𝑥 − (2 + 4𝑥) = 90 − 4𝑥 + 𝑥
g.
|𝑥 − 4| = 24