Intro To Statistics - Chapter 4

Front 1

Data in which a single variable is measured.

Back 1

Univariate Data

Front 2

Data in which two variables are measured.

Back 2

Bivariate Data

Front 3

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

Back 3

Response Variable

Front 4

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.

Back 4

Scatter Diagram

Front 5

Two variables that are linearly related have this type of association when above-average values of one variable are associated with above-average values of the other variable and below-average values of one variable are associated with below-average values of the other variable. That is, whenever the value of one variable increases the value of the other variable also increases.

Back 5

Positively Associated

Front 6

Two variables that are linearly related have this type of association when above-average values of one variable are associated with below-average values of the other variable. That is, whenever the value of one variable increases the value of the other variable decreases.

Back 6

Negatively Associated

Front 7

A measure of the strength and direction of the linear relation between two quantitative variables.

Back 7

Linear Correlation Coefficient or Pearson product moment correlation coefficient. The Greek letter ρ (rho) represents the population correlation coefficient, and r represents the sample correlation coefficient.

Front 8

Formula for Linear Correlation Coefficient

Back 8

Where:

x̄ is the sample mean of the explanatory variable.

Sx is the sample standard deviation of the explanatory variable.

Ybar is the sample mean of the response variable.

Sy is the sample standard deviation of the response variable.

n is the number f individuals in the sample.

Front 9

Computational Formula for Linear Correlation Coefficient

Back 9

Front 10

Formula for Slope

Back 10

m=(y2-y1)/(x2-x1)

Front 11

The point where the graph of the line crosses the y-axis

Back 11

Y intercept

Front 12

Point Slope Formula

Back 12

y-y1=m(x-x1)

Front 13

Straight Line Equation

Back 13

y = mx + b

Where m is the slope and b is the y-intercept

Front 14

The difference between the observed and predicted values of y.

Back 14

The error or Residual.

Front 15

The line that minimizes the sum of the squared errors (or residuals). This line minimizes the sum of the squared vertical distance between the observed values of y and those predicted by the line, ŷ (y hat). We represent this as "Minimize Σ residuals²".

Back 15

Least-Squares Regression Line

Front 16

Equation for Least Squares Regression Line

Back 16

ŷ = b1x + b0

Where b1 = r(sy/sx) is the slope of hte least-squares regression line

and

b0 = y-bar - b1x̄ is the y-intercept of the least squares regression line.

Front 17

Computational Formula for Least Squares Regression Line

Back 17