Question

1. Explain the meaning of independent and dependent variable.

2. What is the difference between correlation and regression analysis?

3. An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices (in RM thousands) of these cars.

Age, x 8 3 6 9 2 5 6 3
Price, y 45 210 100 33 267 134 109 235


a. Construct a scatter plot for the data.                   
b. Comment on the relationship between age and price of cars base on the above scatter plot of the data.              
c. Calculate the correlation coefficient, R. Interpret the calculated value of R.
d. Calculate the correlation of determination. Interpret the value of R2.
e. Briefly comment on the relationship between the two variables based on the correlation coefficient, R.                 
f. Calculate the slope, b.
g. Calculate the intercept, a.
h. Write the regression equation.


Key Formulas
Coefficient of Correlation
R =∑( )(Y −Y ) Standard deviation, x Standard deviation, y Slope of the regression line X − X
(n−1)s sx y 2 ∑ y−y)2                 =Rb Sy
(x−x) (
s =x ∑n−1 s =y n−1 Sx
Intercept of the regression line    Linear Regression Equation            a = Y bX -            Y a= +   bX

        

Answer 1

1. Independent variable: The variable that is used to predict another variable. Its value is not dependent on any other variable.

Dependent variable: The variable whose value needs to be predicted and depends on another variable.

2. Correlation tells whether there exists a relationship between two variables. Regression magnitude the strength of this relaationship.

3. Using Excel, Insert Scatter Plot. Right-click on any point, select Add trendline, choose Linear. Tick Display Equation on Chart and Display R-squared value.

a. scatter plot

b. positive linear relationship

c. correlation coefficient, R = 0.9717^0.5 = 0.986

There exists a strong positive relationship between age and price.

d. correlation of determination = 0.972

97.2% variation in price is explained by age.

e. There exists a strong positive relationship between age and price.

f. Slope: b= -34.443

g. Interept: a = 322.45

h. y = 322.45 - 34.443x