Question

KPMG is trying to identify a linear relationship that can be used to estimate the heating costs for its commercial properties. Below is a table showing heating costs and floor area for a sample of five buildings in the area. Floor Area and corresponding heating costs Floor Area - (1000s sq. ft.) Heating - Cost ($1000s) 50 310 80 300 90 420 110 410 120 460 The slope of the least squares line is 2.2. The intercept is 182. Construct a 95% confidence interval estimate of E(y200), the expected heating cost for the set of all buildings that have 200,000 square feet of floor space. Report the upper bound for the interval.

Answer 1

The estimated heating cost for a building with 200,000 square feet of floor space is 622 thousand dollars.

Step-by-step explanation:

In order to construct a 95% confidence interval estimate of E(y200), the expected heating cost for buildings with 200,000 square feet of floor space, we can use the least squares line equation. The equation of the line is given by: Heating Cost = 182 + 2.2 * Floor Area. Plugging in the floor area of 200,000 square feet, we can calculate the expected heating cost.

Heating Cost = 182 + 2.2 * 200 = 182 + 440 = 622 thousand dollars

Therefore, the estimated heating cost for a building with 200,000 square feet of floor space is 622 thousand dollars.

Answer 2

To construct a 95% confidence interval estimate of the expected heating cost for buildings with 200,000 square feet of floor space, we can use the equation of the least squares line. The upper bound for the 95% confidence interval estimate is 659.08.

Step-by-step explanation:

To construct a 95% confidence interval estimate of E(y200), the expected heating cost for buildings with 200,000 square feet of floor space, we can use the equation of the least squares line. The equation is y = mx + b, where y represents the heating cost and x represents the floor area. The slope (m) is 2.2 and the intercept (b) is 182. Plugging in x = 200, we can calculate the estimated heating cost:

E(y200) = 2.2(200) + 182 = 604

Now, to find the upper bound of the confidence interval, we need to find the margin of error. The formula for the margin of error is given by:

Margin of Error = t * (Standard Error)

Since we need a 95% confidence interval, we can find the t-value for a two-tailed test at a significance level of 0.05 and four degrees of freedom (n-2=3). Using a t-table or calculator, we find t = 3.182. The standard error can be calculated as:

Standard Error = sqrt((sum of squared residuals) / (n-2)) = sqrt(300) = 17.32

Finally, plugging in the values, we get:

Margin of Error = 3.182 * 17.32 = 55.08

Therefore, the upper bound for the 95% confidence interval estimate of E(y200) is:

E(y200) + Margin of Error = 604 + 55.08 = 659.08