Linear Regression

How can you determine the type of correlation from a scatterplot?

• By observing the color of the points

• By observing the direction of the points: upward for positive, downward for negative, and scattered for no correlation.

• By counting the number of points in the scatterplot

• By measuring the distance between the points

How do you interpret a slope of 2 in a linear regression equation?

• A slope of 2 means that for every one unit increase in x, y increases by 2 units.

• A slope of 2 indicates that y decreases by 2 units for every one unit increase in x.

• A slope of 2 suggests that there is no relationship between x and y.

• A slope of 2 means that y increases by 1 unit for every two units increase in x.

What is Linear Regression?

• A statistical method to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

• A technique used to predict categorical outcomes based on independent variables.

• A method for clustering data points into groups based on similarity.

• A process of reducing the dimensionality of data for easier visualization.

What does a positive association in a graph indicate?

• A positive association indicates that as one variable increases, the other variable also tends to increase.

• A positive association indicates that as one variable increases, the other variable tends to decrease.

• A positive association indicates that there is no relationship between the variables.

• A positive association indicates that both variables remain constant regardless of changes.

What is the slope in a linear regression equation?

• The slope represents the rate of change of the dependent variable for each unit change in the independent variable.

• The slope is the point where the line intersects the y-axis.

• The slope indicates the maximum value of the dependent variable.

• The slope is the average of the independent variable values.

What is the significance of the correlation coefficient in linear regression?

• It measures the average of the dependent variable.

• It indicates the strength and direction of the linear relationship between two variables, ranging from -1 to 1.

• It determines the slope of the regression line.

• It assesses the variance of the independent variable.

What does it mean if the linear regression equation is y = 3x + 5?

• This means that for every unit increase in x, y increases by 3, and when x is 0, y is 5.

• This means that for every unit increase in x, y decreases by 3, and when x is 0, y is 5.

• This means that for every unit increase in x, y increases by 5, and when x is 0, y is 3.

• This means that for every unit increase in x, y increases by 3, and when x is 0, y is 0.

What does a negative association in a graph indicate?

• A negative association indicates that as one variable increases, the other variable tends to decrease.

• A negative association indicates that both variables increase together.

• A negative association indicates that both variables decrease together.

• A negative association indicates that one variable has no effect on the other.

How can outliers affect a linear regression analysis?

• Outliers can improve the accuracy of the regression model.

• Outliers can skew the results of a linear regression analysis, potentially leading to misleading conclusions about the relationship between variables.

• Outliers have no effect on the regression analysis.

• Outliers can only affect the intercept of the regression line.

What does 'no association' mean in a scatterplot?

• It indicates a strong positive relationship between the two variables.

• It means that there is no discernible relationship between the two variables; changes in one do not predict changes in the other.

• It shows that one variable is dependent on the other.

• It suggests a negative correlation between the two variables.