# Regression & Correlation Flashcards

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The regression line has a negative slope: when *x* values increase, the corresponding *y* values decrease and *r*, the correlation coefficient, is negative.

The slope of the regression line is positive: as the *x* values increase, the *y* values also increase and the correlation coefficient, *r*, is positive.

One event is the cause of another event.

This is when a relationship exists between two events, but one event does not cause the other.

This assumes that the residuals follow a normal distribution around the line of best fit.

This assumes that around the regression line, the variance in the values of the independent variable is the same.

This assumes that there is a linear relationship between the independent and dependent variables.

In this assumption, the residuals vary randomly and do not follow a pattern.

A process for studying how variables are related in a statistical sense.

What you get when you find the difference between predicted and observed values.

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## Flashcard Content Overview

This lesson covers the statistical concepts of correlation and causality as encountered when performing a regression analysis on a set of data. Skills covered are how to determine:

- the slope of the regression line
- the intercept of the regression line
- the correlation coefficient

Key terms include residual, statistical independence, linearity, homoscedasticity, negative correlation, positive correlation, variance and normality.

What you get when you find the difference between predicted and observed values.

A process for studying how variables are related in a statistical sense.

In this assumption, the residuals vary randomly and do not follow a pattern.

This assumes that there is a linear relationship between the independent and dependent variables.

This assumes that around the regression line, the variance in the values of the independent variable is the same.

This assumes that the residuals follow a normal distribution around the line of best fit.

This is when a relationship exists between two events, but one event does not cause the other.

One event is the cause of another event.

The slope of the regression line is positive: as the *x* values increase, the *y* values also increase and the correlation coefficient, *r*, is positive.

The regression line has a negative slope: when *x* values increase, the corresponding *y* values decrease and *r*, the correlation coefficient, is negative.

*r*= 0

The variables are not correlated.

*r*

The variables are weakly correlated.

*r*is close to 1

The variables are strongly correlated.

*x*is the charging time in hours, and

*y*is the voltage. When

*x*is 0,

*y*= 8. Write the linear equation for

*y*in terms of

*x*.

*y* = 0.1*x* + 8

where *x* is the charging time in hours and *y* is the voltage

*x*= hours and

*y*= volts. At

*x*= 0,

*y*= 8. This battery's voltage should not exceed 12 volts. When should the charger be turned off?

*y* = 0.5*x* + 8, where *x* is the time in hours and *y* is the voltage. At *x* = 8 hours, the charger should be turned off because *y* will be equal to 12.

*x*and let

*y*be the cost in dollars. Write a linear equation relating

*x*and

*y*.

*y* = 200*x* + 100

*x*= hours building a model,

*y*= model cost. For

*x*= 1, 2 and 3,

*y*= 2, 4 and 8. The data is: (1, 2), (2, 4) and (3, 8). Use the formula for slope,

*a*, and intercept,

*b*, to find the linear model.

*y* = 3*x* - 4/3

First make your chart with columns for x, y, xy, and x^2 and find the sum of each column. Use the formulas for *a* and *b*.

a = [3(34) - 6(14)] / [3(14) - 6^2] = 18/6 = 3

b = 1/3[14 - 3(6)] = -4/3

*y*, for delivery of a gift is related to the amount,

*x*, paid for postage. This data is observed: (10, 15), (20, 10) and (30, 5). Calculate the correlation coefficient,

*r*.

*r* = -1

A plot of *x*-*y* ordered pairs showing how the data in *x* and *y* are related.

*x*is rainfall;

*y*is growth. Intercept is?

The intercept is 0.5. With no rainfall, the growth is 0.5 inches.

*x*= discount rate;

*y*= sales. What is slope?

Slope = 2. For each 0.25 change in discount rate, there will be a 0.5 increase in the number of sales.

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Statistics 101: Principles of Statistics11 chapters | 144 lessons | 9 flashcard sets

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- Overview of Statistics Flashcards
- Summarizing Data Flashcards
- Tables and Plots Flashcards
- Probability Flashcards
- Discrete Probability Distributions Flashcards
- Continuous Probability Distributions Flashcards
- Regression & Correlation Flashcards
- Hypothesis Testing in Statistics Flashcards
- Z-Scores & Standard Normal Curve Areas Statistical Table
- Critical Values of the t-Distribution Statistical Table
- Binomial Probabilities Statistical Tables
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