Question

question 3 (2 points)
use your calculator to find the equation of the line of best fit.
oil production
the table shows the u.s. daily oil production y (in thousands of barrels) x years after 1994
round your answer to the nearest tenth.
y = ____ x + ____
blank 1:
blank 2:
question 4 (1 point)
use your equation from #3 to predict the daily oil production in 2009. round to the nearest tenth.
hint - dont plug in 2009! plug in the years after 1994
y = ______ (thousands of barrels)
blank 1:

Explanation:

Step1: Input data into calculator

Input the \(x\) - values (\(0,1,2,3,4,5,6,7,8\)) and \(y\) - values (\(6660,6560,6470,6450,6250,5880,5820,5900,5750\)) into a graphing calculator.

Step2: Find linear regression equation

Using the linear regression function (\(LinReg(ax + b)\)) on the calculator.
Let \(n = 9\) (number of data points).
The formula for the slope \(a=\frac{n\sum(xy)-\sum x\sum y}{n\sum(x^{2})-(\sum x)^{2}}\) and the \(y\) - intercept \(b=\frac{\sum y - a\sum x}{n}\).
\(\sum x=0 + 1+2+\cdots+8=\frac{8\times(8 + 1)}{2}=36\)
\(\sum y=6660+6560+\cdots+5750 = 55780\)
\(\sum(xy)=0\times6660+1\times6560+2\times6470+\cdots+8\times5750\)
\(=6560 + 12940+19350+25000+31250+29400+34920+41300+46000=247720\)
\(\sum(x^{2})=0^{2}+1^{2}+2^{2}+\cdots+8^{2}=\frac{8\times(8 + 1)\times(2\times8 + 1)}{6}=204\)

\(a=\frac{9\times247720-36\times55780}{9\times204-(36)^{2}}\)
\(=\frac{2229480-2008080}{1836 - 1296}=\frac{221400}{540}\approx - 123.0\)

\(b=\frac{55780-(-123)\times36}{9}=\frac{55780 + 4428}{9}=\frac{60208}{9}\approx6689.8\)

Step3: Predict for \(x = 15\) (since \(2009-1994 = 15\))

Substitute \(x = 15\) into \(y=-123.0x + 6689.8\)
\(y=-123.0\times15+6689.8=-1845+6689.8 = 4844.8\)

Answer:

Question 3:
Blank 1: \(-123.0\)
Blank 2: \(6689.8\)
Question 4:
Blank 1: \(4844.8\)