1. Least Square Regression
More info (as usual)
and
Computer Output with Interpretations

2. Where did it get it’s name?
The sum of all the errors squared is called the total sum of squared errors (SSE).
Calculate the error (residual) and square it.

3. Four Key Properties of LSR
The LSR passes through the point
The LSR sum of residuals is zero.
The LSR sum of residuals squared is an absolute minimum.
The histogram of the residuals for any value of x has a normal distribution (as does the histogram of all the residuals in the LSR)—constant variance.

4. Has the number of flights increased over the past years?
Searching the Internet to find information on air travel in the United States, data was found on a number of commercial aircraft flying the United States during the years The dates were recorded as years since Thus the year 1990 was recorded as year 0.

5. Has the number of flights increased?

6. Flights
r =
r2 =

7. Flights—Computer Output
Predictor Coef Stdev t-ratio p
Constant
Years
s = 33.43
Write the LSR equation from the computer output?
Flights = (Years) –

8. How tall is that building if you know how many stories are in it?
46 “tall” buildings were selected from all over the US.

9. How tall is it? 198.6 ft 45 Is this a decent model? Why or why not?
If a building had 10 stories, what would its height be?
If a building stood 600 ft tall, how many stories would it have?
198.6 ft 45

10. Is there a relationship between body weight and height?
200 students’ body weight and corresponding height are in this sample.

11. Height to Weight?

12. Height to Weight? LSR Equation y-intcp slope P-value
The regression equation is WEIGHT = HEIGHT
Predictor Coef Stdev t-ratio p
Constant
HEIGHT
s = R-sq = 61.6% R-sq(adj) = 61.2%
Analysis of Variance
SOURCE DF SS MS F p
Regression
Error
Total
Unusual Observations
Obs. HEIGHT WEIGHT Fit Stdev.Fit Residual
slope
P-value

13. Check for bell-shaped (normal) histogram of residuals
Height to Weight?
Check residual plot of residuals vs. height
Check for bell-shaped (normal) histogram of residuals

14. Height to Weight?

15. Four Key Properties of LSR
The LSR passes through the point
HEIGHT Mean
WEIGHT Mean
The LSR sum of residuals is zero.
SUM Residuals =
The LSR sum of residuals squared is an absolute minimum.
SUM Squared Residuals =
The histogram of the residuals for any value of x has a normal distribution (as does the histogram of all the residuals in the LSR)—constant variance.

16. Height to Weight? Hypothesis Testing of Slope, 1: Ho: 1= 0 Ha: 1 0
Predictor Coef Stdev t-ratio p
Constant
HEIGHT
Since the p-value is less than .05, we reject the null hypothesis and conclude that the slope does not equal zero.

17. Limitations to Predictions
Interpolation
Extrapolation
Confidence Intervals estimate the mean value of the response variable for a particular value of x.
Prediction Intervals (like confidence intervals) are used to describe the variation among individuals with a particular value of x.