Shown below is a portion of a computer output for a regression analysis relating
ID: 3428553 • Letter: S
Question
Shown below is a portion of a computer output for a regression analysis relating Y (demand) and X (unit price).
Summary Output
Regression Statistics
Multiple R 0.786
R Square 0.617
Adjusted R Square 0.609
Standard Error 8.252
Observations 48
a.
Please write out the estimated regression line.
b.
Determine whether or not demand and unit price are related. Let ? = 0.05.
c.
What is the coefficient of determination and fully interpret its meaning.
d.
Compute the coefficient of correlation and explain the relationship between demand and unit price.
Explanation / Answer
a. Please write out the estimated regression line.
Y (demand) = 80.390 - 2.137* X (unit price).
b
Determine whether or not demand and unit price are related. Let a = 0.05.
Calculated t = -8.610, P=0.000 <0.05 level.
The null hypothesis of regression coefficient = 0 is rejected.
We conclude that demand and unit price are related.
c.
What is the coefficient of determination and fully interpret its meaning.
coefficient of determination =0.617
61.7% of variance in the variable demand is explained by the variable unit price.
d.
Compute the coefficient of correlation and explain the relationship between demand and unit price.
Given = Multiple R = 0.786
The sign of the regression coefficient = negative
the coefficient of correlation = - 0.786
There is negative relation between demand and unit price.
When unit price increases the demand decreases or unit price decreases the demand increases.