Question

Consider the following results of a simple regression model of dollar price of unleaded gas (dependent variable) and dollar price of crude oil (independent variable):

Coefficient	t-statistics
Intercept	0.56	28.27
Crude Oil	0.0457	73.34

R-square = 0.87

1. What will be expected change in the price of unleaded gas if the crude oil price is expected to fall by 7%. The current price of crude oil and unleaded gas are $74 and $3.10 respectively?

1. (7.89%)
2. (6.85%)
3. (7.25%)
4. (7.64%)

2. What will be forecasted price of unleaded gas if the crude oil price is expected to fall by 3%. The current price of crude oil and unleaded gas are $74 and $3.10 respectively?

1. $3
2. $2.93
3. $2.86
4. $3.07

3. What is the interpretation of coefficient for crude oil?

1. Every $1 increase in crude price will cause unleaded gas price to increase by 4.57 cents.
2. Every $1 increase in crude price will cause unleaded gas price to increase by 4.57 %.
3. Every 1% increase in crude price will cause unleaded gas price to increase by 4.57%.
4. Every 1% increase in crude price will cause unleaded gas price to increase by 4.57 cents.

4. What will be forecasted price of unleaded gas when the crude oil price is $80?

1. $3.99
2. $4.44
3. $4.22
4. $4.67

Answer 1

a.

The regression equation is,

Unleaded gas = 0.56 + 0.0457 crude oil price

If the crude oil price is expected to fall by 7%, then,

New Unleaded gas = 0.56 + 0.0457 crude oil price * (1 - 0.07)

Change in Price = New Unleaded gas - Unleaded gas

= (0.56 + 0.0457 crude oil price) - (0.56 + 0.0457 crude oil price * (1 - 0.07))

= 0.0457 crude oil price * 0.07

= 0.0457 * 74 * 0.07

= 0.236726

Expected percent change = (Change / Unleaded gas price) * 100

= (0.236726 / 3.10) * 100

= 7.636323 %

d. (7.64%)

b.

The regression equation is,

Unleaded gas = 0.56 + 0.0457 crude oil price

If the crude oil price is expected to fall by 3%, then,

  New Unleaded gas = 0.56 + 0.0457 crude oil price * (1 - 0.03)

Change in Price = New Unleaded gas - Unleaded gas

= (0.56 + 0.0457 crude oil price) - (0.56 + 0.0457 crude oil price * (1 - 0.03))

= 0.0457 crude oil price * 0.03

= 0.0457 * 74 * 0.03

= 0.101454

Forecasted price of unleaded gas = 3.10 - 0.101454

= 3

a. $3

c.

Slope of the regression line = 0.0457

Every $1 increase in crude price will cause unleaded gas price to increase by $0.0457 = 4.57 cents

Thus,

a. Every $1 increase in crude price will cause unleaded gas price to increase by 4.57 cents.

d.

The regression equation is,

Unleaded gas = 0.56 + 0.0457 crude oil price

For crude oil price = $80

Unleaded gas = 0.56 + 0.0457 * 80 = 4.216

c. $4.22