Unit 4 - Activity 1 - Scatter Plots and Linear Correlation Worksheet Scatter plot: a graph drawn to show the relationship between two variables.~ Linear correlation: variables are said to have a linear correlation when the changes in one ~ variable are proportional to changes in the other variable.~ Linear regression: the technique for finding the equation with the form y = ax + b that best ~ figures the relationship between the x (independent) and y variables (dependent).~ Correlation Coefficient, 1: the measure of correlation between two variables, it determines how well a regression line fits a set of data. Dependent variable: also known as the response variable (y-axis). Independent variable: is also known as the explanatory variable (x-axis). Classifying Linear Correlations:Positive or Direct Correlations a) b) yA C) YA Strong Linear Moderate Linear Weak Linear ~ Negative or Inverse Correlations d) yA e) YA 1) y4 Zero/No Linear Correlation Strong Linear Moderate Linear Weak Linear Correlation Coefficient, r:. A value between -1 and 1+ . A negative value represents negative correlation . A positive value represents positive correlation . 0 represents no correlation -1/+1 represent perfect negative/positive linear correlation n(Exy) - (Z x) (Zy) VIn(Ex?) - (Ex)'][n(Zy=) -(Zy)'] Example 1 A farmer wants to determine whether there is a relationship between the mean temperature during the growing season and the size of his wheat crop. He assembles the following data for the last six crops.~ Mean Temperature ("C) Yield (tonnes/hectare) 1.60 2.40 T. 2.0- 90 2.60 2.10 2.2+ a) Draw a scatter plot of the data and indicate if there is any linear correlation between the 2 variables.~b) Compute the correlation coefficient. What can the farmer conclude about the relationship between the mean temperatures during the growing season and the wheat yields on his farm?~ Temperature, x Yield, yo 1.64 xy+ 2.40 2.04 T. 2.64 L L L Ittt 114 2.10 L t t t t 2.24 T