unit 3 - ch 13 - simple linear regression (slr)

Question 1

Underlying all is for slr is

Answer 1

chance

Question 2

Chance

Answer 2

Correlation is passive (is)
Chance is application (of)
Are they moving in tandem (x and y)

Data always varies during to reason or chance
Chance is foundation in which regression is built

Question 3

number of sales for six salesperson (SP)

Answer 3

We don’t know how much each salesperson sold

Number of sales → Y variable
Guess each salesperson’s sales?
Rule: You must guess the same number for each person

Your guess?
The mode → 10 (guess 6 times)
Right 2/6 times

Question 4

How much error with each guess?

Answer 4

E = Y-10 (guess)

Question 5

total error –> ess –> error sum of the square

Answer 5

Ess mode = sigma (Y-10)^2

Question 6

comparison of guesses

We want to limit our losses but it’s like golf.. It’s not that we’re gonna hit a hole in one but what we want is to make multiple good shots to eventually get to the whole

Answer 6

Limit your losses not just a whole in one
Not really really wrong
Guessing the mean is this.. Limiting our losses
Substitute the word usually for average
How much better can we do than guessing we build off of this

Question 7

predictions

Answer 7

Guessing to predictions
X is new here

Is the x variable and y variable correlated?

Use fx function to get r value
r = 0.92.18

Use fx function for intercept
b = 2.0909

Use fx function for the slope
m = 0.8182
Line of best fit

Question 8

line

Answer 8

y = mx + b

Question 9

regression equation (line of best fit)

Answer 9

y hat = b + mx

y hat = predicted value
b = y-intercept
m = slope

example
y hat = 2.0909 + 0.8182(x)

Question 10

FM = full model

Answer 10

Using all predictive variables (x variables)

In SLR = 1 predictive variable (FM)
Chance model had no predictive variable
Full model all predictive variables
Line of best fit

Question 11

SLR: common business practices

Answer 11

Predicting and/or forecasting
>Hiring decisions
>Inventory cycles
>Future sales

Understanding underlying elements
>Marketing strategy
> Operation efficiency

Supplement executive creativity
> Reveal new insights

Question 12

SLR: Looking for relationships, making associations, drawing conclusions
Example of assumptions:

Answer 12

Outfit → Purchasing Power
Job → Disposition
Car → Personality

Question 13

residuals (there is no perfect model)

Answer 13

Residuals woo!!!
Residual is another name for error

Question 14

line of best fit - on exam (multiple questions)

Answer 14

memorize the picture in notes!!!!!!!!!

Question 15

Line of best fit not perfect fit

Answer 15

Only would happen if there would be a perfect correlation
If r = +/- 1 or e = 0 there would be a perfect fit

Question 16

Residuals (error) =

Answer 16

Residuals (error) = Y - Y hat
e = actual - predicted
e not r

Question 17

Ordinary least squares regression =

Answer 17

Ordinary least squares regression = less total error

Doesn’t care if error is positive or negative, cares about magnitude of error
Sigma (Y-Y hat)^2 (squaring!!!!)

Errors are often plotted either randomly or normally

Question 18

properties and qualities of residuals (error)

Answer 18

notation: a sample –> e, for a population –> funny looking e

if r = +1 or -1, e = 0

ordinary least squares regression: total error decrease

sum(y-yhat) = 0, always!, so sigma(y-yhat)square

sum(y-yhat)square –> total error: 7.81

Question 19

plot errors

Answer 19

randomly scattered around the x-axis
normally distributed
randomly scattered around the x-axis

> more errors as you draw closer to x-axis (in the middle)
model is reducing the error that is why
in taking random samples our error should be random

Question 20

plots and data point

Answer 20

If data point fall out in some sort of pattern you do not have a linear regression. Relationship can be parabolic etc. but it is not linear

If residuals fall out in a pattern it is not linear

Question 21

chance model vs full model

Answer 21

??????

FM = full model
Using all predictive variables (x variables)
In SLR = 1 predictive variable (FM)
Chance model had no predictive variable
Full model all predictive variables
Line of best fit

Question 22

Total variation in the Y-variable can divided into 2 distinct components:

Answer 22

Regression term
Y’s relationship with the X-variable(s)
Picked up in full model (has x in the formula)

Residual term
Random factors not in the model (error)
Years of experience, gender, age etc. that are not int he model that can influence sales of salesperson etc.

Question 23

Four Key Concepts for SLR
Concept 1: The coefficient of determination

Answer 23

coefficient of determination- RSQ - the percentage of the variation in the y-variavle that is explained by the variation in the x-variables

Don’t confuse the coefficient of determination (RSQ) with the correlation coefficient (r, p)
A percentage
range = 0-1
Practical because percentages are understandable

Question 24

square r

Answer 24

r = 0.9218
RSQ = about 85%
How high does RSQ need to be

Useful in context = good RSQ
Human behavior RSQ is lower because behavior is complex

Question 25

rsq: context

Answer 25

higher rsq = context

Question 26

Four Key Concepts for SLR
Concept 2: Isolating the slope

Answer 26

The affect of marginal inputs on predicted outcomes
Example: Major league baseball
Y = Wins
X = Payroll (USD, millions)
Y hat = 67 + 0.04(x)

Question 27

q1: how much does each win– above what the regression model provides– cost?

q2: if mlk team owner increases payroll b y 100 million, fans can expect what marginal affect on wins

(look at notes)

Answer 27

Hint: Rise over run (isolating the slope)

Q1 =$25 (USD, millions)
Q2 = 4 more wins

Question 28

Regression toward the mean:

Answer 28

extreme outcomes tend to be followed by moderate outcomes
Small samples have more variation than large ones

Question 29

Four Key Concepts for SLR
Concept 3: Over and under performing the model

(look at notes to see overperforming vs underperforming)

Answer 29

e = Y - Yhat

Y above the line: +e
Y below the line: -e

red circle: overperforming teams
black circles: underperforming teams

Question 30

Four Key Concepts for SLR
Concept 4: The Restricted Model

(look at notes)

Answer 30

a) CM: no predictor variables
House example: Beach house
Money lending
“How much can you lend”
“Let me guess”
“?”
CM is for comparison purposes only not for use in practice

b) FM: all predictor variables

c) RM: some predictor variables (get prequalified by loan officer)

Question 31

why use a restricted model

Answer 31

Why use a restricted model?
RM works well enough
RM is less complicated
RM is cheaper

Question 32

Linear regression for two variables is based on a linear equation with one independent variable. The equation has the form:

Answer 32

y = a + bx

Question 33

regression analysis

Answer 33

Regression analysis is a statistical technique that can test the hypothesis that a variable is dependent upon one or more other variables. Further, regression analysis can provide an estimate of the magnitude of the impact of a change in one variable on another. This last feature, of course, is all important in predicting future values.

Regression analysis is based upon a functional relationship among variables and further, assumes that the relationship is linear. This linearity assumption is required because, for the most part, the theoretical statistical properties of non-linear estimation are not well worked out yet by the mathematicians and econometricians