When estimating the cost of building a new house, Karmax Builders calculates $70 per square foot, $3,500 for miscellaneous expenses. What’s the slope of the equation?

Summarize the meaning of the slope in the context of the problem

Step-by-step explanation:

70 is the slope.

70 represents the cost of one square foot.

Per every square foot (x), the cost increases by 70 (y).

The amount of square feet changes the total cost.

Equation is represented as:

3500 represents the y-intercept.

70 represents the slope.

The answers to the question are

(a) The time series plot is given as attached

(b) The parameters for the line that minimizes MSE for the time series are;

y-intercept, b₀ = 19.993

Slope, b₁ =  1.77

MSE = 19.44

T = 19.993  + 1.774·t

(c) The average cost increase that the firm is realizing per year is $ 1.77

(d) The estimate of the cost/unit for next year is $35.96.

Step-by-step explanation:

(a) Using the provided data, the time series plot is given as attached

(b) Given hat the y-intercept, = b₀

Slope = b₁

Therefore the  linear trend forecast equation is given s

T = b₀ + b₁·t

The linear trend line slope is given as

b₁ =

b₀ = - b₁·

Where:

Y = Time series plot value at t

n =  Time period number

= Time series data average value and

= Average time, t

Therefore, =

= 4.5

 =  

 =  27.975

Therefore the linear trend line equation T, is

b₁ = =   = 1.774

b₀ = - b₁· = 27.975 - 1.774×4.5 = 19.993

Therefore the trend equation for the linear trend is

T = 19.993  + 1.774·t

MSE = = = 19.44

(c) From the linear trend equation, the average is given as the slope of the curve or b₁ which is equal to 1.774

Therefore the average cost increase that the firm has been realizing per year is $ 1.77

(b) From the equation of the future trend, we have when y = 9

T  is given as

T = 19.993  + 1.774×9 = 35.96

The cost/unit for 9th year is $35.96