Regression and Scatterplots

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run). It can be positive, negative, zero, or undefined.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship between the two variables.

Front

What does a slope of zero mean?

Back

A slope of zero means that the line is horizontal, indicating that there is no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs in a vertical line, where the change in x is zero, leading to division by zero.

Front

How do you find the equation of a line given two points?

Back

To find the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then use the point-slope form: y - y1 = m(x - x1).

Front

What is a scatterplot?

Back

A scatterplot is a graph that displays values for typically two variables for a set of data, showing how much one variable is affected by another.

Front

What does a scatterplot with a linear pattern suggest?

Back

A scatterplot with a linear pattern suggests a linear relationship between the two variables, meaning they can be described by a straight line.

Front

What is correlation in statistics?

Back

Correlation measures the strength and direction of a linear relationship between two variables, ranging from -1 (perfect negative) to +1 (perfect positive).

Front

What is a strong positive correlation?

Back

A strong positive correlation means that as one variable increases, the other variable also tends to increase significantly.