unit 3 - ch 13 - multiple linear regression (mr)

Question 1

The multivariate dependent and independent relationship

Answer 1

Y - carat
X - price of gem
X2 - cut
X3 - clarity
X4 - Color

Question 2

The multiple regression equation

Answer 2

Y hat = b + mx +

MR = Y hat = (y hat equation)
Partial or correlation coefficient is that middle part

Question 3

Dummy variables

Answer 3

Using categorical (nominal) data
Converts categorical data into binary data
Used for _____ (missed in lecture)
Gem - Y - X1 - X2
Non-numeric data = text
0-1 binary code

Question 4

r

Answer 4

Sign is - or +
Range is -1 or +1
Direction is indicates
X-y relationship is =

Question 5

multi r

Answer 5

Sign is +
Range is 0 to +1
Direction is does not indicate
X-y relationship is >=
Multi-r is a single point-value representing the strength of a simultaneous relationship between the x-variables and Y

Question 6

(multi) collinearity

Answer 6

Share
Line (slope)
(Multi) collinearity:
When 2 (or more) x-variables are highly correlated with each other

The mutli-variate dependents (X and Y)
Independent relationships (X and X)

Question 7

multi-variate dependent vs independent relationships

Answer 7

The mutli-variate dependents (X and Y)
Independent relationships (X and X)

Question 8

student car broke down on campus

Answer 8

Student X moves car (Y) across campus.
The total distance of the movement of car (Y) is 100% due to the effort of student (X) = simple linear regression

Next day students (X1 and x2) move car (Y)
We can measure the total distance car (Y) was pushed by harder to find efforts of X1 AND X2 STUDENTS ADD TO THE TOTAL MOVEMENT OF TOTAL

r or multi r formula

Question 9

The adverse effects of multicollinearity

Answer 9

When 2 or more x-variables are highly correlated
1. Cannot decipher which x-variable is affecting the y-variable (not an issue with SLR)
2. Increase the chances of type 2 error (FTRN that is really false)
3. The signs of the partial correlation coefficients may flip

As collinearity decreases there is an increase in each predictor variables unique portion of the variability within the Y-variable

Question 10

Multiple regression excel:

regression table
anova table
collinearity table

Answer 10

r = Strength
a = Significance
c = Collinearity

Question 11

the strength of the relationship: summary output table (regression table)

Answer 11

Coefficient of determination: the percent of the variation in gem price that is explained by the variation in carat, cut, clarity, color

N= sample size
P = number of predictors
If the general rule regarding sample size is not met adjusted R square is a more accurate indicator of the strength of the multiple regression relationship

Question 12

judgment call

Answer 12

Is the strength of the relation (missed again) :(
Multiple R, R square, Adjusted RSQ → Strength of the relationship → judgment call

Question 13

test stat =

Answer 13

= between term/within term

Question 14

underlying theory of anova test

Answer 14

total variation can be divided into two distinct parts:
1 - between AND
2 - whtin (error)

and the two components can be compared to determine which is affecting the data to a greater degree

Question 15

total variation in the y-variable can be divided into distinct components

Answer 15

regression. term
residual term (error)

Question 16

regression term

Answer 16

1 - regression term (Y’s relationship with the X-variable)

Regression term: Y hat - Y bar

Question 17

residual term

Answer 17

2 - residual term (random factors not in the model)

Residua Term: Y - Y hat

Question 18

full model

Answer 18

FM = Y hat = b + m(x)

Question 19

total variation

Answer 19

Total Variation: Y - Y bar

Question 20

increase of F

Answer 20

increase ms regression / decrease ms residual

Question 21

decrease of F

Answer 21

decrease ms regression / increase ms residual

Question 22

anova table

Answer 22

1 of the 4 facets of the Null states: everything is unrelated

Ho: The model of caret, cut, clarity, and color is unrelated with gem price
H1: The model of caret, cut, clarity and color is correlated with gem price

If FTRN: the model is not significantly correlated to the Gem price (is not a good model)
If RTN: the model is significantly correlated to Gem price (is statistically good model)

Question 23

when to FTRN or RTN

Answer 23

If FTRN: the model is not significantly correlated to the Gem price (is not a good model) F>a

If RTN: the model is significantly correlated to Gem price (is statistically good model) F<a

Significance F is compared to alpha not p value and RTn or FTRN

Question 24

unexplained variation

Answer 24

Naked eye appeal - seller’s reputation, seller’s service etc…
16-17%

Question 25

explained variability

Answer 25

Carat, cut, clarity, color etc.
83-84%

Question 26

The value of the chance model is not for practical use but for

Answer 26

comparison purposes

Question 27

significance of the components

Answer 27

Y hat = b0 + b1 (x1) + b2 (x2) + b3 (x3) + e….

b0 = y-int
b1 = (partial) correlation coefficient
e1 = residual

1 of the 4 facets of the Null states: everything is unrelated
Ho: each x-variable is not correlated with gem price
H1: each x-variable is correlated with gem price

IF FTR: the x-variable is not a good predictor variable
If RTN: the x-variable is a good predictor variable

Question 28

p value vs alpha (FTRN vs RTN)

Answer 28

P value < alpha : reject
P-value > alpha : FTRN

Question 29

0 and 1 variable

Answer 29

The “0” variable:
Reference group
Represents the absence the qualitative attribute

The “1” variable:
Dummy variable
Represents the presence the qualitative attribute

Question 30

look at notes i guess to understand graphs :/

Answer 30

If the gem is pink, rather than green, it demands a premium
Pink gems, on average, cost (…)

If dummy coefficient was a negative number: pink gems sell t a discount compared to green gems