Question 1: When making predictions using the line of best fit, the prediction for a new data point is obtained by extending the line to the desired x-value and reading off the corresponding y-value. The accuracy depends on the closeness of data points to the line.

Answer: Use the line of best fit to predict y at a given x by extending the line and reading off the value.

Question 1: Plot the line of best fit for the following data points: (1, 2), (2, 4), (3, 6), (4, 8).

Answer: A straight line passing through the points, roughly y=2x.

Question 2: Using the line y=2x, predict the y-value when x=5.

Answer: 10

Question 3: A data set has a line of best fit y=1.5x + 1. Using this line, predict y when x=0.

Answer: 1

Question 4: Explain why a prediction made at an x-value far from the data points might be less accurate.

Answer: Because the line of best fit is less reliable outside the range of data, predictions may be inaccurate due to extrapolation errors.

Question 5: Identify and correct the mistake in this statement: 'The line of best fit perfectly predicts all data points.'

Answer: The line of best fit approximates data; it does not predict all points exactly.

Question 6: Given the scatter plot shows data with a positive trend, which of the following is the most appropriate line of best fit? A) Horizontal line, B) Downward sloping line, C) Upward sloping line.

Answer: C

Question 7: A student fits a line to data but notices many points are far from the line. What might this indicate?

Answer: The line may not be appropriate, or there may be outliers; the model's accuracy could be compromised.

Question 8: Construct a line of best fit for the data: (2, 3), (4, 7), (6, 11).

Answer: Line roughly y=2x-1

Question 9: Using your line of best fit from the previous question, predict y when x=8.

Answer: 15

Question 10: A scatter diagram shows a weak correlation. Why might fitting a line of best fit be misleading in this case?

Answer: Because weak correlation means data points are scattered, so the line may not accurately represent the relationship, leading to unreliable predictions.

Question 11: Identify a common mistake when interpreting the line of best fit for making predictions.

Answer: Assuming the line predicts all data points exactly or extrapolating too far beyond data range without caution.

Question 12: What is a more reliable way to assess the accuracy of a line of best fit before making predictions?

Answer: Check the correlation coefficient or analyze residuals to evaluate how well the line fits the data.