What you’ll learn
Estimate a line of best fit.
Key idea
A reasonable fitted line approximates the cloud; its slope uses vertical change divided by horizontal change.
An approximate line need not pass through every observation; do not claim a unique least-squares optimum.
Worked example
Enter the exact value or ordered values in the format requested below.
Observed scatter pairs {(0,3),(1,8),(2,11),(3,14),(4,19)} have a supplied reasonable fitted line through guidepoints ((0, 3), (4, 19)). Estimate that line's slope; enter the number.
- The supplied reasonable trend line y=4x+3 has guidepoints ((0, 3), (4, 19)); slope=(19-3)/(4-0)=4.
- For predicted y=11, x=(11-3)/4=2. Observed residuals (0, 1, 0, -1, 0) show balanced small departures, not an exact interpolating requirement.
Answer: 4
Quick Check
Evaluate a worked attempt at estimate a line of best fit, identify the first invalid step, and provide the correction.
Observed pairs {(0,7),(1,10),(2,11),(3,12),(4,15)}, supplied fit y=2x+7: Step 1 uses guidepoints ((0, 7), (4, 15)). Step 2 obtains slope 2. Step 3 rejects the fit solely because the x=1 observation is off the line. Locate the first invalid step and correct it.