The graph in Exercise 64 shows the number of student y enrolled in public colleges for selected years x , where x is the number of years since 1990. The table gives a partial list of data from the graph. a. Use the data in the table to find the least-squares regression line. Round the slope to 2 decimal places and the y -intercept to 1 decimal place. b. Use a graphing utility to graph the regression line and the observed data. c. Assuming that the linear trend continues use the model from part (a) to predict the number of students enrolled in public colleges for the year 2020. d. By how much do the results of part (c) differ from the result of Exercise 64(d)?
The graph in Exercise 64 shows the number of student y enrolled in public colleges for selected years x , where x is the number of years since 1990. The table gives a partial list of data from the graph. a. Use the data in the table to find the least-squares regression line. Round the slope to 2 decimal places and the y -intercept to 1 decimal place. b. Use a graphing utility to graph the regression line and the observed data. c. Assuming that the linear trend continues use the model from part (a) to predict the number of students enrolled in public colleges for the year 2020. d. By how much do the results of part (c) differ from the result of Exercise 64(d)?
Solution Summary: The author calculates the least squares regression line by rounding the slope to 2 decimal and y-intercept.
The graph in Exercise 64 shows the number of student y enrolled in public colleges for selected years x, where x is the number of years since 1990. The table gives a partial list of data from the graph.
a. Use the data in the table to find the least-squares regression line. Round the slope to 2 decimal places and the y-intercept to 1 decimal place.
b. Use a graphing utility to graph the regression line and the observed data.
c. Assuming that the linear trend continues use the model from part (a) to predict the number of students enrolled in public colleges for the year 2020.
d. By how much do the results of part (c) differ from the result of Exercise 64(d)?
A factorization A = PDP 1 is not unique. For A=
7 2
-4 1
1
1
5 0
2
1
one factorization is P =
D=
and P-1
30
=
Use this information with D₁
=
to find a matrix P₁ such that
-
-1 -2
0 3
1
-
- 1
05
A-P,D,P
P1
(Type an integer or simplified fraction for each matrix element.)
Matrix A is factored in the form PDP 1. Use the Diagonalization Theorem to find the eigenvalues of A and a basis for each eigenspace.
30 -1
-
1 0 -1
400
0
0 1
A=
3 4 3
0 1 3
040
3 1 3
0 0
4
1
0
0
003
-1 0 -1
Select the correct choice below and fill in the answer boxes to complete your choice.
(Use a comma to separate vectors as needed.)
A basis for the corresponding eigenspace is {
A. There is one distinct eigenvalue, λ =
B. In ascending order, the two distinct eigenvalues are λ₁
...
=
and 2
=
Bases for the corresponding eigenspaces are {
and ( ), respectively.
C. In ascending order, the three distinct eigenvalues are λ₁ =
=
12/2
=
and 3 = Bases for the corresponding eigenspaces are
{}, }, and {
respectively.
University Calculus: Early Transcendentals (4th Edition)
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