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The response variable is the variable whose value can ..., Slides of Statistics

Gonzaga UniversityStatistics

The response variable is the variable whose value can be explained by the value of the explanatory or predictor variable.

Typology: Slides

2022/2023

Uploaded on 03/01/2023

elmut
elmut 🇺🇸

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Lesson6:IntrotoCorrelationandRegression
The
responsevariable
isthevariablewhose
valuecanbeexplainedbythevalueofthe
explanatory
or
predictorvariable
.
Let'sbeginwithimportantterminology:
A
scatterdiagram
isagraphthatshowstherelationshipbetweentwo
quantitativevariablesmeasuredonthesameindividual.
Eachindividualinthedatasetisrepresentedbyapointinthescatter
diagram.
Theexplanatoryvariableisplottedonthehorizontalaxis,andtheresponse
variableisplottedontheverticalaxis
.
example)
Drawandinterpretascatterplot.
Watchvideotoseethisdoneonthecalculatorinrealtime.
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Lesson 6: Intro to Correlation and Regression The response variable is the variable whose value can be explained by the value of the explanatory or predictor variable. Let's begin with important terminology: A scatter diagram is a graph that shows the relationship between two quantitative variables measured on the same individual. Each individual in the data set is represented by a point in the scatter diagram. The explanatory variable is plotted on the horizontal axis, and the response variable is plotted on the vertical axis. example) (^) Draw and interpret a scatterplot. Watch video to see this done on the calculator in real time.

Two variables that are linearly related are positively associated when aboveaverage values of one variable are associated with aboveaverage values of the other variable and belowaverage values of one variable are associated with belowaverage values of the other variable. That is, two variables are positively associated if, whenever the value of one variable increases, the value of the other variable also increases. Two variables that are linearly related are negatively associated (^) when aboveaverage values of one variable are associated with belowaverage values of the other variable. That is, two variables are negatively associated if, whenever the value of one variable increases, the value of the other variable decreases.

Properties of the Linear Correlation Coefficient

  • The^ linear^ correlation^ coefficient^ is^ always between –1 and 1, inclusive. That is, –1 ≤ r ≤
  • If r = + 1, then a perfect positive linear relation exists between the two variables.
  • If r = –1, then a perfect negative linear relation exists between the two variables.
  • The closer r is to +1, the stronger is the evidence of positive association between the two variables.
  • The closer r is to –1, the stronger is the evidence of negative association between the two variables.
    • If r is close to 0, then little or no evidence exists of a linear relation between the two variables. So r close to 0 does not imply no relation, just no linear relation.
    • The linear correlation coefficient is a unitless measure of association. So the unit of measure for x and y plays no role in the interpretation of r.
    • The correlation coefficient is not resistant. Therefore, an observation that does not follow the overall pattern of the data could affect the value of the linear correlation coefficient.

let's revisit the drilling data remember we made a scatterplot...well now let's compute the linear correlation coefficient: ex) If you are really interest in crunching r by hand see below...watch my video to see it done on the calculator and excel.