Question

7. Consider the following sample regression equation = 150 – 20x, where y is the demand for Product A (in thousands) and x is the price of the product A (in $).

a) What is the value of the correlation coefficient when the R2 value for the above equation is 0.65?

b) What kind of relationship is there between y and x? Describe the strength and direction.

c) Estimate the demand for Product A when the price is $5?

d) At what price will there be no demand for Product A? e) What happens to demand as price increases? f) Interpret the slope.

Answer 1

Given that the sample regression equation = 150 – 20x,

where,

y = The demand for Product A (in thousands)

x =The price of the product A (in $).

a) Given R-squared value = 0.65

The correlation Coefficeint is Sqrt(0.65) = -0.806225

b) Slope = -20 which is < 0

therefore, Demad of product A and price of product A is negative relation.

i.e. As demand increase price decrease and vice-versa.
The strength of the correlation is 0.65 = 65%

c) If price = $5 then
Demad Y-hat = 150 -20 * 5

= 150-100

= 50

d) If demand = 0 then price will be
y-hat = 0
150-20x = 0
-20x = -150
x = -150/-20

x=7.5

i.e. if Price is $7.5 there be no demand for product A.

e) If price increase then demand decrease
Since, there exist negative correlation between them.

f) As price increase $1 then demand decrease 20 units
Since, Slope = -20