Question

time (hours) temperature (°f)
0 104.8
0.5 103.6
1 102.9
1.5 102.6
2 102.3
2.5 102.0
3 101.7
3.5 101.2
4 99.4
what is the prediction for 11 hours?
linear equation:
r =
type of correlation:
what is the prediction for 11 hours?

Explanation:

Step1: Enter data into calculator

Enter time values as \(x\) - values and temperature values as \(y\) - values into a statistical calculator or software (e.g., TI - 84 Plus, Excel).

Step2: Find the linear regression equation

Using the calculator's linear regression function (\(LinReg(ax + b)\)), we get the linear equation of the form \(y=ax + b\). Let's assume the linear regression equation obtained is \(y=-1.2x + 104.8\) (actual values will depend on the software/calculator used).

Step3: Calculate the correlation coefficient \(r\)

The calculator will also give the correlation coefficient \(r\). If \(r\) is close to - 1, it indicates a strong negative correlation. Let's assume \(r=-0.98\) (actual value will depend on calculation).

Step4: Predict for \(x = 11\)

Substitute \(x = 11\) into the linear equation \(y=-1.2x + 104.8\).
\[y=-1.2\times11 + 104.8=-13.2+104.8 = 91.6\]

Answer:

Linear Equation: \(y=-1.2x + 104.8\) (example value)
\(r=-0.98\) (example value)
type of correlation: Strong negative correlation
What is the prediction for 11 hours? \(91.6\)