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- Pennsylvania
- Pennsylvania State University - All Campuses
- Statistics
- Statistics 200
- Buchanan
- Exam 2 Review

E L.

Conservative Margin of Error [for categorical v]

1/sqrt.n *where n=sample size

*margin of error= measure of accuracy of a sample population

-the amount by which the sample proportion differs from the true population proportion is less than this quantity in at least 95% of all random samples.

usually reported in percentages (x 100)

*margin of error= measure of accuracy of a sample population

-the amount by which the sample proportion differs from the true population proportion is less than this quantity in at least 95% of all random samples.

usually reported in percentages (x 100)

Sample Size & Margin of Error

You can gauge the opinion of millions in a brief sample of 1500 by within 3%

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Positively Associated Variables

*When the values of one variable tends to increase as the value of the other variable increases

EX: tall people and hand size

EX: tall people and hand size

Negatively Associated Variables

*When the values of one variable tend to decrease as the values of the other variable increase

Linear Relationship

When the relationship pattern of two variables resembles a straight line

Curvilinear

When a curve describes the pattern of a scatterplot better than a line does

Regression Analysis

*used to examine relationship between a quantitative response variable and one of more explanatory variables

Regression Equation

Describes how, on average, the response variable is related to explanatory variables

*can predict response variable using known values of explanatory variable

EX: equation between verbal SAT score and college GPA. Could use the equation to PREDICT potential GPA's of students.

*can predict response variable using known values of explanatory variable

EX: equation between verbal SAT score and college GPA. Could use the equation to PREDICT potential GPA's of students.

Regression Line

A straight line that describes how values of a quantitative response variable (y) are related on average, to values of quantitative explanatory variable (x)

*THE LINE IS USED FOR:

1. estimating the average value of y at any specified value of x

2. predicting the value of y for an individual, given that individual's x value

*THE LINE IS USED FOR:

1. estimating the average value of y at any specified value of x

2. predicting the value of y for an individual, given that individual's x value

Equation of a Straight Line

relating to y and x is:

y=b_{0} + b_{1}x

b_{0}= y intercept

b_{1}=_{ }slope

Handspan= -3 +0.35 (Height)

y=b

b

b

Handspan= -3 +0.35 (Height)

Interpreting the Slope

Measures how much the y variable changes per each one-unit increase in the value of the x variable

Handspan= -3 +0.35 (Height) **THIS means that handspan increases by .35 cm on average for each 1 in increase in height. we can estimate avg. diff in handspan bc if heights differ by 7 inches do [7 x .35= 2.45 cm] difference in handspans is approx 1 i.

Handspan= -3 +0.35 (Height) **THIS means that handspan increases by .35 cm on average for each 1 in increase in height. we can estimate avg. diff in handspan bc if heights differ by 7 inches do [7 x .35= 2.45 cm] difference in handspans is approx 1 i.

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Prediction Errors

difference between observed y-value and predicted y-value (y-yhat)

Residuals

the more neutral term for the difference between (y-yhat) [observed y value - predicted y-value]

Least Squares

Basis for estimating equation of regression line

"least sum of squared errors"

"least sum of squared errors"

Correlation

between two quantitative variables, this is the number that indicates strength and direction of a straight-line relationship

- the
**strength of the relationship**is determined by the**closeness of the points to a straight line** - the
**direction**is determined by whether one variable generally increases or decreases when the other variable increases

Correlation

- represented by "r"
- measures sometimes called "correlation coefficient"
- doesn't matter which variable is x and which is y
- Correlation coefficients
**always**between -1 and +1 - a correlation of -1 or +1 indicates a perfect linear relationship and all data points fall on the same straight line
- correlation of 0 indicates that the best straight line thru data is horizontal

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