# STA 205 Lecture Notes - Lecture 13: Dependent And Independent Variables, Point Estimation, Prediction Interval

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develop alinear model that

can be used for prediction

and estimate

response the variable we

want to model ly

dependent

perdictor the variable

hypothesised to have an

effect on the response x

independent

Packet 13: Correlation & Regression

After completing this material, you should be able to:

• identify the response and predictor variables

• interpret a scatterplot in context

• obtain the correlation from StatCrunch and interpret the strength of the linear relationship

• use StatCrunch output to obtain the line of best fit and interpret the coefficients (where appropriate)

• use a hypothesis test to determine if there is a significant linear relationship between two variables

• use the regression equation for prediction

• interpret the appropriate interval (confidence interval or prediction interval) for a given scenario.

Goal:

Because we now have two quantitative variables collected, we need a way to distinguish between them:

response variable:

predictor variable:

Example: A consumer organization would like to develop a model to predict a car’s gas mileage (in miles per gallon) based

upon its weight (in thousands of pounds). In order to do this, a random sample of 50 cars was selected with weights

ranging between 1900 pounds and 4000 pounds.

What two variables were recorded for this sample of 50 cars?

To graphically inspect the relationship between these two variables, we can create a scatterplot. When given a

scatterplot, the following three characteristics should be

discussed:

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Aweight lbs if gas mileage gal

predictor response

direction of the

relationship

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1direction of the relationship

positive as ary9

negative as xRYd

2type of relationship

pattern

linear

non linear

3unusual observations

that Do Not follow the

trend