Line of Best Fit/ Least Squares Regression Line

This applet will let you explore the slope of the predicted line of best fit and how it affects the least square regression.
Question 1: a) Move the slider (a) around to change the slope. Is the slope positive or negative? b) Predict where the line of best fit will be and record the slope value. Question 2: a) What is the sum of squares when the slope is zero (found in the spreadsheet)? b) Set the slope value to the prediction you made in 1b. What is the sum of the squares that is shown in the spreadsheet? c) Can you change the slope value to make the sum of the squares a smaller value? If so, record the value of the slope and the sum of the squares stated in the spreadsheet. Question 3: a) How does the slope of the Line of Best fit relate to your slope value found in 2c? b) Explain the similarity or difference between your slope value and Geogebra's best fit slope value. Question 4: a) How does the sum of the areas of the squares from 2a relate to the sum of the areas from 2d? b) Can you predict the depth of the coin dropped into water at 45 seconds? c) How about at 100 seconds?