Shown below is a portion of a computer output for a regression analysis relating

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.

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