Advanced Algebra II Notes 3.5 Residuals

Residuals: y-value of data point – y-value on the lineExample: The manager of Big K Pizza must order supplies for the

month of November. The numbers of pizzas sold in November during the past four years were 512, 603, 642, and 775, respectively. How many pizzas should she plan for this November?

Step 1: Put the x values into List 1, and the y-values into List 2. Do a scatter plot of the data. Step 2: On the home screen, press STAT, right arrow to CALC, down arrow to Med-Med, ENTER. Step 3: Press 2nd 1, a comma, 2nd 2, a comma, VARS, right arrow to Y-VARS, enter on Function, and again on Y1. Step 4: Copy the equation into the chart above, and using that equation, find f(1), f(2), f(3) and f(4). Step 5: Find the residuals and enter into the chart. Step 6: What is the sum of the residuals? What should it be? Step 7: What does it mean if the sum of the residuals is positive? Negative?

Year (x) 1 2 3 4# pizzas (y)

Y-value from lineY=

Residual: (see above definition of residuals)

Root Mean Square Error: A measure of the spread of data points from a model.

represents the y-values of the data pairs

represents the y-values of the model (equation)

2

)(1

2^

n

yys

n

iii

iy^

iy

What does this appear to be similar to?

Example B: A scientist measures the current in milliamps through a circuit with constant resistance as the voltage in volts is varied. Make a scatter plot of the data, use the regression capability of the calculator to find:Linear regression equation: __________________________

b) Median-Median equation: __________________________ Complete the table below:

Voltage(x)

5 7.5 10 12.5 15 17.5 20

Current(y)

2.354 3.527 4.698 5.871 7.053 8.225 9.403

Linear RegPrediction

Residual

Med-Medprediction

Residual

residual2

residual2

2yy

1yy

To use the calculator to compute the residuals: Step 1: In List 3 command (highlight L3) enter Step 2: In List 4 command: (L3)2

Step 3: 2nd STAT, right arrow to MATH, down arrow to sum(L3) enter. Step 4: Divide Step 3 by (n-2) Step 5: Take the square root of Step 4. According to residuals, which is the best fit?

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