Exploring Linear Regression and Best Fit Lines

What is the primary goal of linear regression?

• To identify outliers in a dataset

• To calculate the median of a dataset

• To determine the relationship between two variables

• To find the average of two variables

When drawing a line of best fit, what is a general guideline to follow?

• Ensure there are as many data points above the line as below it

• Ensure all data points are below the line

• Ensure all data points are above the line

• Ensure the line passes through the origin

How do you determine the equation of a best fit line manually?

• By averaging the x and y values

• By using the median of the data points

• By selecting two points on the line and calculating the slope and intercept

• By using the mean of the data points

What is the purpose of using a calculator for linear regression?

• To calculate the median of the data points

• To identify outliers in the data

• To determine the exact best fit line using sophisticated techniques

• To find the average of the data points

What does the linear correlation coefficient (R value) indicate?

• The strength and direction of the linear relationship between two variables

• The number of data points

• The median of the data points

• The average of the data points

What is interpolation?

• Identifying outliers in the data

• Using a model to predict values outside the range of observed data

• Using a model to predict values within the range of observed data

• Calculating the average of the data points

Why is extrapolation considered more dangerous than interpolation?

• It always provides accurate predictions

• It involves predicting values outside the range of observed data

• It is easier to perform than interpolation

• It involves predicting values within the range of observed data

In the practical example, what is the least squares regression equation used for?

• To calculate the median weight of salmon

• To find the average length of salmon

• To relate the length of steelhead salmon to their weight

• To identify outliers in the salmon data

What is the expected weight of a salmon that is 30 inches long using the given regression equation?

• 39.51 pounds

• 1.33 pounds

• 27.98 pounds

• 9.35 pounds

Which part of the practical example involved interpolation?

• Predicting the weight of a salmon that is 52 inches long

• Predicting the weight of a salmon that is 30 inches long

• Calculating the average weight of salmon

• Identifying outliers in the salmon data