Bi-Variate Data

Honors Analysis

Univariate and Bivariate Data  Univariate data: Data of a single data type. (Ex: Test scores, number of wins, age of family members, salaries of employees, etc.)  Bivariate data: A set of data comparing pairs of values in an ordered pair. Generally used when a relationship exists between the two data types.

***Does not necessarily imply causality!

Scatter Plots  You can show relationships between two variables using a scatter plot.

Correlation – how closely the data follows a pattern

Correlation Coefficient -- r  Your graphing calculator can calculate a value r, called the Pearson Product-Moment Correlation. It is a value between -1 and 1 that describes the linearity of a data set.

 If r = 1, the data forms a perfect linear relationship with a positive slope. If r = -1, it forms a perfect linear relationship with a negative slope.

 1 𝑟 = 𝑛−1 (𝑥 1 −𝑥) (𝑦 1 −𝑦) + 𝑠 𝑥 𝑠 𝑦 (𝑥 2 −𝑥) (𝑦 2 −𝑦) + ⋯ 𝑠 𝑥 𝑠 𝑦

Examples of r values and scatter plots

Writing Linear Equations – Point Slope Form

𝑦 − 𝑦

1

= 𝑚(𝑥 − 𝑥

1 )

Writing Line of Best Fit Equations  Least-squares linear regression is a process often used to write best fit equations.

 The central concept is trying to find the smallest error (called the residual between each point and the line.

 Your graphing calculator allows you to determine linear regression lines using the LinReg function.

Constructing a Confidence Interval for a Sample Proportion  Calculate the standard deviation for the sample: 𝑠𝑑 = 𝑛  The standard deviation for the sample proportion is often called the Margin of Error (ME)

Constructing a Confidence Interval for a Sample Proportion  Determine the confidence level. You can estimate 68% confidence using ±1𝑀𝐸 , 95% confidence using ±2𝑀𝐸 , and 99% using ±3𝑀𝐸 .  For a more specific confidence level, you will need to use your table of z-scores to find create the desired confidence.

𝑍 ∗ , the number of std. dev. above/below the mean to

Constructing a Confidence Interval for a Sample Proportion   To calculate a more specific confidence interval, determine scores).

𝑍 ∗ (you may want to sketch a picture of the interval and then use your table of z Confidence Interval: ∗ 𝑛

Calculating Confidence Intervals  It is also possible to use the formula for ME to determine the sample size required to attain a desired confidence level.