Understanding the y-intercept and slope

What is the Y-intercept?

The y-intercept is where a line crosses the vertical axis (y-axis) on a graph. It’s the starting point of the line when the horizontal value (x) is zero.

Example: Imagine you’re looking at how education affects income. The y-intercept might represent someone’s income with zero years of education. For instance, if the y-intercept is £15,000, it means someone with no formal education might earn £15,000 per year on average.

What is the Slope?

The slope shows how steep a line is on a graph. It tells us how much one thing changes when another thing changes.

The slope formula is:

Slope = (Change in Y) / (Change in X)

Social Science Examples

1. Voting and Age.
   • Y-intercept: The percentage of 18-year-olds who vote (the starting point).
   • Slope: How much the voting percentage increases for each year of age.
2. Social Media Use and Happiness.
   • Y-intercept: Happiness level of someone who doesn’t use social media.
   • Slope: How happiness changes with each hour of daily social media use.
3. Income and Years of Experience.
   • Y-intercept: Starting salary for a new graduate.
   • Slope: How much salary increases for each year of work experience.

Understanding the slope: Linear Regression

[y = mx + c]

Where:

• m is the slope of the line (how steep it is).
• c is the y-intercept (where the line crosses the y-axis).
• y is your y value (the value of the dependent variable).
• x is your x value (the value of the independent variable).

Visualising Linear Regression

When we plot points and draw a regression line:

1. Each point represents a piece of data (x, y).
2. The line shows the overall trend.
3. The distance between each point and the line shows how accurate our predictions are.

Examples in Social Science

Linear regression can be used in many ways, such as:

Voter Turnout

• X-axis: Average income in a community.
• Y-axis: Percentage of people who voted.

This can show if higher income leads to higher voter turnout.

Campaign Spending

• X-axis: Money spent on a campaign.
• Y-axis: Percentage of votes received.

This helps to see if spending more money results in more votes.

In Simple Terms

• The y-intercept is like the starting point of a journey.
• The slope is like how fast you’re moving on that journey.

Together, they help us understand and describe how things are related in the social world around us.