7.4 Linear Regression Lesson Check

Front

What is the linear regression equation for a dataset?

Back

A linear regression equation is a mathematical representation of the relationship between two variables, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope in a linear regression equation represent?

Back

The slope represents the rate of change of the dependent variable (y) for each unit increase in the independent variable (x).

Front

What does the y-intercept in a linear regression equation indicate?

Back

The y-intercept indicates the value of the dependent variable (y) when the independent variable (x) is zero.

Front

How do you interpret the slope of the equation y = 1.5x + 12?

Back

The slope of 1.5 means that for each additional topping on a pizza, the price increases by $1.50.

Front

What is the significance of the y-intercept in the equation y = 30.5x + 110?

Back

The y-intercept of 110 indicates that the initial club fee is $110 when no games of golf have been played.

Front

What is the equation of the line of best fit?

Back

The equation of the line of best fit is a linear equation that best represents the data points in a scatter plot.

Front

What does a negative slope indicate in a linear regression model?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

What is the formula for calculating the slope (m) between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the term 'line of best fit' refer to?

Back

The line of best fit is a straight line that best represents the data on a scatter plot, minimizing the distance between the line and all data points.

Front

How can you determine if a linear regression model is a good fit for the data?

Back

A good fit can be determined by analyzing the correlation coefficient (R²), residual plots, and how well the model predicts new data.