Question

The following table indicates the monthly cost of electricity against air –conditioning temperature in a household:

AC Temperature (degree Celsius 25 23 21 19 17 Cost of Electricity
(Pesos) 3000 3300 3500 3800 4000
a. Compute for the b₀ and b₁ in the regression equation
b. Give the regression equation c. Predict the cost of electricity if the AC is set at a temperature of 16℃ in a month.

Answer 1

a. The value of b₀ and b₁ in the regression equation -61.05 and 5890.75 respectively

b.The regression equation is y = 5890.75 - 61.05x

c. The predicted cost of electricity if the AC is set at a temperature of 16℃ is 4893.95 Pesos.

Step-by-step explanation:

a. To compute for b₀ and b₁ in the regression equation, we need to perform linear regression analysis using the given data. The regression equation is in the form of y = b₀ + b₁x, where y represents the cost of electricity and x represents the AC temperature.

Using the given data, we can calculate the values of b₀ and b₁ using the following formulas:

b₁ = (n∑(x*y) - ∑x * ∑y) / (n∑(x²) - (∑x)²)

b₀ = (∑y - b₁∑x) / n

Let's calculate the values of b₀ and b₁:

n = number of data points = 5

∑x = sum of AC temperatures = 25 + 23 + 21 + 19 + 17 = 105

∑y = sum of costs of electricity = 3000 + 3300 + 3500 + 3800 + 4000 = 17600

∑(x*y) = sum of (AC temperatures * costs of electricity) = (25*3000) + (23*3300) + (21*3500) + (19*3800) + (17*4000) = 375500

∑(x²) = sum of (AC temperatures squared) = (25^2) + (23²) + (21²) + (19²) + (17²) = 2165

Using these values, we can now calculate b₀ and b₁:

b₁ = (5*375500 - 105*17600) / (52165 - 105²) = -61.05

b₀ = (17600 - (-61.05)105) / 5 = 5890.75

b. The regression equation is y = b₀ + b₁x. Substituting the calculated values, we have:

y = 5890.75 - 61.05x

c. To predict the cost of electricity if the AC is set at a temperature of 16℃, we can plug in the value of x into the regression equation:

y = 5890.75 - 61.0516 = 4893.95

Therefore, the predicted cost of electricity if the AC is set at a temperature of 16℃ is 4893.95 Pesos.

Answer 2

• a. The value of b₀ and b₁ in the regression equation -61.05 and 5890.75 respectively
• b.The regression equation is y = 5890.75 - 61.05x
• c. The predicted cost of electricity if the AC is set at a temperature of 16℃ is 4893.95 Pesos.

Step-by-step explanation:

a. To compute for b₀ and b₁ in the regression equation, we need to perform linear regression analysis using the given data. The regression equation is in the form of y = b₀ + b₁x, where y represents the cost of electricity and x represents the AC temperature.

Using the given data, we can calculate the values of b₀ and b₁ using the following formulas:

b₁ = (n∑(x*y) - ∑x * ∑y) / (n∑(x²) - (∑x)²)

b₀ = (∑y - b₁∑x) / n

Let's calculate the values of b₀ and b₁:

• n = number of data points = 5
• ∑x = sum of AC temperatures = 25 + 23 + 21 + 19 + 17 = 105
• ∑y = sum of costs of electricity = 3000 + 3300 + 3500 + 3800 + 4000 = 17600
• ∑(x*y) = sum of (AC temperatures * costs of electricity) = (25*3000) + (23*3300) + (21*3500) + (19*3800) + (17*4000) = 375500
• ∑(x²) = sum of (AC temperatures squared) = (25^2) + (23²) + (21²) + (19²) + (17²) = 2165

Using these values, we can now calculate b₀ and b₁:

b₁ = (5*375500 - 105*17600) / (5*2165 - 105²) = -61.05

b₀ = (17600 - (-61.05)*105) / 5 = 5890.75

b. The regression equation is y = b₀ + b₁x. Substituting the calculated values, we have:

y = 5890.75 - 61.05x

c. To predict the cost of electricity if the AC is set at a temperature of 16℃, we can plug in the value of x into the regression equation:

y = 5890.75 - 61.05*16 = 4893.95

Therefore, the predicted cost of electricity if the AC is set at a temperature of 16℃ is 4893.95 Pesos.