Question

Use quadratic regression and a graphing calculator to find the quadratic function that best fits the data set. Then use the model to forecast the value of the function at the indicated point. (Round your coeffiecients to two decimal places.) Years Since 1985 Abortion:s (per 1000 live births) 0 5 10 15 16 17 422 389 350 324 325 319 What was the abortion rate in 2007? (Round your answer to the nearest whole number.) abortion:s

Answer 1

from the x coordinate

matrix A and A^T are

.

6 5 0 3 0 050567 051111

.

from the y coordinate

vector b is

422 389 350 324 325 919

.

take $\large A^T*A$

Ar A-(0 5 10 15 16 İ7)| 1 10 3 0510151617ノ1115 1 16 1 17

/6 63 895 ATA= 895

..

.

now take $\large A^T*b$

422 389 350 0 5 10 15 16 17 324 325 319 1 1

АТЬ (O 1424225-1389 910-3300 15 324 +16 3225 11731319) 0. 422+5 . 389+ 10. 350+ 15. 324 + 16. 325+17. 319

2129 ( 20928 "47 b

.

.

solve for $\large [A^T*A]x=[A^T]b$

2129 20928 63 895m

augmented matrix is

6	63	2129
63	895	20928

convert into Reduced Row Eschelon Form...

Divide row1 by 6

1	21/2	2129/6
63	895	20928

Add (-63 * row1) to row2

1	21/2	2129/6
0	467/2	-2853/2

Divide row2 by 467/2

1	21/2	2129/6
0	1	-2853/467

Add (-21/2 * row2) to row1

1	0	586991/1401
0	1	-2853/467

reduced matrix is

3 1 0

586991 1401 13883

.

.

line is y=mx+c

.

${\color{Red} y=-\frac{2583}{467}x+\frac{586991}{1401}}$

.

or

${\color{Red} y=--5.53x+418.98}$

.

.

in 2007 take x=22

.

y - 5.53 - 22 + 418.98

${\color{Red} y= 297}$.............asnwer