Unit 2 Flashcards

1
Q

What is a scatterplot used for

A

Immediate visual impression of a possible relationship between 2 variables.

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2
Q

What is the correlation coefficient

A

Used as a quantitative value of strength and direction of a linear relationship.

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3
Q

Inequality of value of correlation coefficient and symbol

A

-1 < r < 1

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4
Q

What is r^2

A

Coefficient of determination - % of variation in the resp var that is explained by the explanatory var

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5
Q

How is r^2 represented

A

As a %

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6
Q

what does 100% r^2 mean

A

Perfect fit

all variation in x

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7
Q

How to describe a scatter plot and eg

A

Direction
Form
Strength

Strong positive linear association

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8
Q

What are the boundaries of r (what value of r is strong, etc)

A

r > 0.8 = strong
0.7 < r < 0.8 = moderately strong
r < 0.7 = weak

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9
Q

What is a residual

A

Difference between an observed and predicted value

= actual - predicted

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10
Q

Sum and mean of residuals is always equal to

A

0

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11
Q

Line of regression eqn and what each variable is

A

y hat = a + bx

a = y intercept
b = slope
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12
Q

How to calculate B

what does each variable mean

A

r * sy/sx

r = correlation coeff
sy = SD of y
sx = SD of x
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13
Q

How to check if linear model is a good fit

A

r^2 should be high

Residual plot shouldn’t show any pattern

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14
Q

How and whyto transform a graph

A

Use log or ln on one of the variables, may allow for a linear model to be used

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15
Q

How to assess the effectiveness of transformation

A

Checking if randomness in residual plot has increased

Checking if r^2 value has increased

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16
Q

What is the LSRL

Full form

A

Least squared regression line

Linear model that minimizes the sum of squared

17
Q

If residuals is negative then

if residuals is positive then

A

Negative - overestimated the response var

Positive - underestimated the response var

18
Q

what is the response var

A

The dependent var

19
Q

What is the explanatory var

A

the independent var

20
Q

How to use residual plot to assess good fit (criteria)

A

Random
Centered at 0
No clear patterns

21
Q

What does a residual plot do

A

Helps decide if you should use a linear model or should consider others.

22
Q

What is extrapolation

why is it bad

A

Prediction that was made outside the interval of current data x values.
Trends may not continue at this next X value so it may not be accurate.

23
Q

How to interpret slope

A

For every ‘x units’ of ‘independent var’, model predict an average increase of ‘slope value’ of ‘dependent var units’

24
Q

How to interpret y intercept

A

When ‘explanatory var’ = 0, model predicts that the ‘resp value’ woudl be ‘y int value’

25
How to interpret r^2
'r^2' percent of var in 'resp var' can be explained by the linear relationship with the 'explanatory var'
26
If r^2 is closer to 0 then | if r^2 is closer to 1 then
r^2 closer to 0 = weak relationship | r^2 closer to 1 = strong relationship.
27
If slope is positive then r is
Positive
28
What is a high leverage point if removed then what what does it change
Points with unusually large or small x values far away from xbar (mean of x values) Cause a substantial shift in the model being used Slope or y int could be changed.
29
What does an outlier affect
R R^2 Strength of the model
30
What is an influential point 3 types what do they affect
Points that when removed change the slope, y int and/or correlation coeff substantially Outliers (corr) High lvg pt (change slope/y int) both of the above