Final answer:
The types of variables needed for a simple linear regression analysis are a numeric response (dependent variable) and a numeric predictor (independent variable). The line of best fit and correlation coefficient are used to analyze the relationship between the variables.
Step-by-step explanation:
The types of variables needed to conduct a simple linear regression analysis are a numeric response (dependent variable) and a numeric predictor (independent variable).
a. The independent variable represents the predictor variable, which we use to explain or predict the values of the dependent variable.
b. To visually analyze the relationship between the variables, we can draw a scatter plot where the x-axis represents the independent variable, and the y-axis represents the dependent variable.
c. By performing regression analysis, we can find the line of best fit which represents the relationship between the variables and the correlation coefficient (r) which measures the strength and direction of the linear relationship.
d. The correlation coefficient indicates the degree of association between the two variables. If the correlation coefficient is close to 1 or -1, it suggests a strong linear relationship. If the correlation coefficient is close to 0, it suggests a weak or no linear relationship.
e. To determine whether there is a linear relationship between the variables, we can examine the scatter plot and the correlation coefficient.