Question

A department store associate wants to find out if there is a relationship (and what kind of relationship) between the price of an item and the time that it takes to a customer to decide in buying that item.

Item Price (x)	Decision Time (in minutes) (Y)
$25	12
$20	8
$300	37
$80	20
$72	15
$25	10
$17	9
$63	14
$140	20
$250	30
$10	4
$8	5
$170	27
$280	28

NOTE: you might be able to get all the necessary information from the scatter plot. You don’t need to do computations by applying the numeric formula.

1. Using Excel construct a scatter plot. Discuss the output of the scatter plot.

2. Give (or calculate) the correlation coefficient.

3. Give (or calculate) the coefficient of determination.

4. Give (or calculate) the regression equation coefficients; Give the equation of regression.

e. (very important)

Based on the above values, in detail draw the conclusion:

• Discuss the correlation coefficient r
• Discuss the coefficient of determination r²
• Discuss in detail the meaning of the regression equation
• How long the decision of buying will take if the item costs $90.00?

Answer 1

a) Scatter plot of the data shows that it is positive linear plot.

Output using excel:

Regression Statistics
Multiple R	0.958146
R Square	0.918045
Adjusted R Square	0.911215
Standard Error	3.039733
Observations	14
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1242.049	1242.049	134.4212	7.09E-08
Residual	12	110.8797	9.239975
Total	13	1352.929
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	7.412886	1.163611	6.370586	3.55E-05	4.877595	9.948178
Item Price (x)	0.092616	0.007988	11.59402	7.09E-08	0.075211	0.110021

b) Correlation coefficient, r = 0.9581

c) Coefficient of determination, r² = 0.9180

d) Slope, b = 0.092616
y-intercept, a = 7.412886

Regression equation :               
ŷ = 7.4129 + 0.0926x

e) Correlation coefficient, r is 0.9581, it shows that the relationship between x any y is strong and positive.

Coefficient of determination, r² = 0.918 is the variation in decision time y that is explained by the linear relationship x and y.

Regression equation :               
ŷ = 7.4129 + 0.0926x

Interpretation of slope:

one unit increase in the item price increases the decision time by 0.0926 units.

Interpretation of y-intercept.

y-intercept of this line is the value of y at the point where the line crosses the y axis.

Predicted value of y at X = 90              
ŷ = 7.4129 + 0.0926 * 90 = 15.75 minutes

If the item costs $90, then the decision time will be 15.75 minutes.