Final answer:
To examine quantitative hypotheses using simple and multiple regression, you will need to decide on the independent and dependent variables, draw a scatter plot, calculate the least-squares line, find the correlation coefficient, and interpret its significance. You can then estimate values and determine if a line is the best fit for the data.
Step-by-step explanation:
In order to examine quantitative hypotheses using simple and multiple regression, you need to follow several steps:
Decide which variable should be the independent variable (x) and which should be the dependent variable (y).
Draw a scatter plot of the data to visually analyze the relationship between the variables.
Calculate the least-squares line by fitting a line that best represents the data points.
The equation for the line will be in the form y = a + bx.
Find the correlation coefficient to measure the strength of the relationship between the variables.
The correlation coefficient ranges from -1 to 1, with 1 indicating a strong positive relationship, -1 indicating a strong negative relationship, and 0 indicating no relationship.
Interpret the significance of the correlation coefficient. If the correlation coefficient is close to 1 or -1, it suggests a significant relationship between the variables. If it is close to 0, it suggests no significant relationship.
Using the equation of the least-squares line, you can estimate the average height for different ages or any other desired values.
Analyze the scatter plot and the correlation coefficient to determine if a line is the best way to fit the data. If the relationship between the variables is not linear or the scatter plot shows a curvilinear pattern, a line may not be the best fit.