More on Scatter Plots and Regression
Scatter plots can represent a variety of situations, not just linear relationships.
Insert a line/curve of best fit for each of the following and identify the type of model that best represents the data.
The 3 types of relationships represented above are also represented below. Indicate which type of model would fit best for each.
For each of the following sketch a scatter plot. Based on your sketch decide which form of regression would best model the situation then use your calculator to determine the equation for the line/curve of best fit as well as the correlation coefficient (r and r 2 values for linear and exponential regression or r2 for quadratic).
1. x y 2. x y 3. x y
3 3.5 -2 0.5 70 187
4 2 0 1 68 167
5 0.1 2 5 66 163
6 1.5 5 30 63 136
7 3
For each of the following determine the equation for the line/curve of best fit using (i) linear regression (ii) quadratic regression and (iii) exponential regression as well as the correlation coefficient (r and r 2 values for linear and exponential and r 2 for quadratic) for each. When you have found all the equations and correlation coefficients indicate which model ‘fits’ the best for each.
4. x y 5. x y 6. x y
10 100 0 5 - 20 120
0 5 3 35 - 12 - 5
15 70 5 55 - 8 - 25
20 1 7 75 7 200
10 105
For each of the following determine the equation for the line of best fit using (i) linear regression (ii) quadratic regression and (iii) exponential regression as well as the correlation coefficient (r or r 2 value for linear and exponential and r 2 for quadratic). When you have found all the equations and correlation coefficients indicate which model ‘fits’ the best for each part.
1. x y 2. x y 3. x y
4. x y 5. x y 6. x y