Question

Consider the following sample regression equation

y hat= 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 R-squared 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

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 = 50

d) If demand = 0 then price will be
y-hat = 0
150-20x = 0
-20x = -150
x=7.5

i.e. if Price is $7.5 there 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