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Hint

1

What is a response variable?

Measures an outcome of a study (dependent variable in a way)

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2

What is an explanatory variable?

Helps to explain or predict changes in a response variable (independent)

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3

What is a scatterplot?

Plot that shows the relationship between two quantitative variables measured on the same individuals.

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4

When describing a scatterplot, what format should you use? Describe Association in Context

Direction: Association (Positive/Negative)

Form: **Approximately **Linear or Curved

Strength: Weak, Medium, Strong

Unusual Features: Outliers

Describe the **Association IN CONTEXT****Example: **Students who took longer to run 40 yards had shorter jump lengths (Association in context). The relationship between the two quantitative variables reveals a positive association while having a linear form, a strong strength. There is one unusual feature at the 25 yard mark, which deviates slightly from the overall pattern.

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5

What does Correlation (r) measure?

The direction and strength of a linear relationship between two quantitative variables. Correlation is always between -1 and 1.

If r>0, the association is positive.

If r<0, the association is negative.

If r=0, the association is none. *This is how you quantify it*.

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6

How would you interpret the r value in context?

Mention the direction and strength!

EX: The R-value of _____ indicates the linear relationship between the number of points scored versus the amount of turnovers is strong and positive.

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7

Facts about correlation….

**It does not imply what caused something!**

Correlation measures strength and direction.

Correlation is not a resistant measure (one point can have a drastic change)

Correlation makes NO distinction of the explanatory and response variable.

Correlation is not affected by data transformations.

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8

What is a regression line?

A line that describes how a response variable (y) changes as an explanatory variable (x) changes. Often used to predict the value of y for a given value of x.

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9

What is the equation of a regression line?

^

y = a +bx

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10

What is extrapolation?

The use of a regression line for prediction far outside the interval of values of the explanatory variable used to obtain the line. **These predictions ARE NOT ACCURATE**

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11

What is a residual? How do you find it?

The prediction error from a regression line. It is the difference between an observed value compared to the predict value.

EQUATION: Residual = Observation-Prediction

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12

What is the Least Squares Regression Line?

A line that makes the sum of the squared residuals as small as possible.

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13

What is a high-leverage point?

A point in an LSRL that has a substantially larger or smaller x-value than the other observations have.

EX: Low X value, high Y value.

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14

What is an influential point?

A point in an LSRL that is any point that, if removed, changes the relationship substantially.

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15

What is the Standard Deviation of the Residuals, s?

The approximate size of a typical prediction error (residual)

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16

How would you interpret a residual?

You state what the residual is (show how you got it), then say if it is above or below the predicted outcome of the response variable.

EX: The residual for the point (8,2) is -14.47, showing that given 8 seconds of tapping time, the result for the amount of soda left (in mL) is 14.47 BELOW the predicted outcome.

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17

Squared deviations determine the _____

Why does the Standard Deviation have to be squared?

LSRL.

If we don’t square the deviations, they will add up to 0.

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18

What happens when you find the mean of the response and explanatory variable, AKA THE 50% mark of each?

They intersect at the LSRL.

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19

What is a residual plot? How do you know which plot to choose?

A scatterplot of the residuals against the explanatory variable. Residual plots help determine whether a linear model is appropriate.

A linear plot can be chosen if there is no pattern.

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20

What is the coefficient of determination (r²)? What is the format?

The fraction of the variation in the values of y that is accounted for by the LSRL of y on x. FORMAT:

______% of the variation in [response variable] is accounted for by the linear (exponential/power) model relating [response variable] to [explanatory variable].

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21

Linear relationships can only be viewed in…

Correlation and Regression

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22

What does the power model equation look like?

^

ln(y) = a+b*ln(x)

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23

What does the exponential model look like?

^

ln(y) = a+b*x

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24

To find the predicted y value for the pwoer model, use the equation:

^

y = e^a+b*log(x)

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25

To find the predicted y value for the exponential model, use the equation:

^

y = e^a+b*x

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26

To find the r-squared value, you do what?

Square the correlation!

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27

How do you interpret the r-squared value?

______% of the variation in [response variable] is accounted for by the linear (exponential/power) model relating [response variable] to [explanatory variable].

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