Understanding Linear Regression and Residuals

What does each dot on a scatter plot represent in the context of height and weight?

• A single measurement of height

• A single measurement of weight

• A person with a specific height and weight

• A trend line between height and weight

What general trend is observed in the scatter plot of height versus weight?

• Height decreases as weight increases

• Weight decreases as height increases

• Height and weight are unrelated

• Height increases as weight increases

What is the purpose of fitting a line to the data in a scatter plot?

• To separate the data into two groups

• To make the plot look more organized

• To find the exact values of height and weight

• To identify the trend and make predictions

What does the 'y hat' symbol represent in the regression line equation?

• The x-intercept of the regression line

• The estimated y value for a given x

• The actual y value for a given x

• The slope of the regression line

What is the y-intercept of the regression line in the given example?

• 140

• -140

• 14/3

• 60

What is the slope of the regression line in the given example?

• 125

• 14/3

• -140

• 60

What is a residual in the context of regression analysis?

• The average of all data points

• The difference between two x values

• The sum of all y values

• The difference between actual and estimated y values

How is a residual calculated for a specific data point?

• By adding the actual and estimated y values

• By subtracting the estimated y value from the actual y value

• By multiplying the actual and estimated y values

• By dividing the actual y value by the estimated y value

What does a negative residual indicate about a data point?

• The actual y value is above the estimate

• The actual y value is below the estimate

• The x value is incorrect

• The data point is an outlier

Why is it important to minimize the squared residuals in regression analysis?

• To make the line as steep as possible

• To achieve the best fit for the data

• To ensure all data points are on the line

• To eliminate all negative residuals