Question

Data Table:

Cost_per_Sq_Foot   1/Sq_Feet

17.54754   0.0000521572
16.32325   0.0000550211
18.22023   0.0000064036
16.65139   0.0000186759
15.61422   0.0000443858
14.92284   0.0000190568
15.57326   0.0000199319
18.41805   0.0000160529
15.75952   0.0004172574
17.47339   0.0002997211
18.41107   0.0000920896
15.35426   0.0000080925
14.83153   0.0000321842
15.71433   0.0002202478
15.14356   0.0001590435
18.19065   0.0004981794
17.44975   0.0001875929
15.77713   0.0000098637
18.31605   0.0001253765
15.42939   0.0000306724
15.51434   0.0000193634
17.70028   0.0000425919
17.16486   0.0000596942
18.14496   0.0000652676
17.81695   0.0001522881
16.23429   0.0001481561
16.99149   0.0000441048
15.57168   0.0000543819
15.57504   0.0000072628
16.82806   0.0000171639
15.43492   0.0000142308
17.97595   0.0000803902
16.94315   0.0000154308
16.77643   0.0000723557
18.02196   0.0001305905
18.58775   0.0001019188
18.15994   0.0000608392
17.41514   0.0000433061
18.62253   0.0000558099
15.86623   0.0000078752
16.38131   0.0000379951
22.19911   0.0004931882
17.31082   0.0000064879
17.55963   0.0001400803
16.41548   0.0001576522
15.53392   0.0000194245
18.04068   0.0002686054
15.85526   0.0002070904
17.37193   0.0000191332
18.34525   0.0001347047

The accompanying dataset includes the annual prices of 50 commercial leases. All of these leases provide office space in a certain city. For the​ response, use the cost of the lease per square foot. As the explanatory​ variable, use the reciprocal of the number of square feet. Complete parts​ (a) through​ (d) below.

​(a) Give a​ 95% confidence interval for the fixed cost​ (the portion of the cost that does not change with the size of the​ lease) of these​ leases, along with a brief interpretation.

The fixed cost is from $__ to $ __ (Round to the nearest dollar as needed)

​(b) Give a 95% confidence interval for the variable cost​ (the cost determined by the number of square​ feet) of these​ leases, along with a brief interpretation.

The variable cost is from $ __ to $ __ (Round to the nearest cent as needed)

(c) How much might a company​ pay, per square​ foot, for a specific lease with 15,000 square feet in this metropolitan​ area? Give a range to show to management. Use a 95% prediction interval.

On​ average, the company would expect to pay from $ __ to $ __ per square foot (Round to the nearest cent as needed)

(d) How much in total might the company pay for a 15,000​-square-foot ​lease? Give a range to show to management. Use a 95% prediction interval.

On​ average, the company would expect to pay from $ __ to $ __ (Round to the nearest dollar as needed)

Note: Show all work and requires the use of JMP Pro program to solve problems quickly

​

​

Answer 1

Linear regression analysis for y = Total cost per lease, and x = square feet would give the below table.

Hence the equation is, Total Cost per Lease(y) = 34.35455 + 16.53699*(Square Feet)

Ans a):

95% confidence interval for fixed cost is given by

[34.354 Critical Value*Standard Error]

For a t-statistic, critical value for n-2 degrees(50-2 = 48) of freedom and 95% confidence interval is 2.01

Hence the range is [34.354 - 2.01*11662.39, 34.354 + 2.01*11662.39]

= [-23407.1,23475.77]

Since the fixed cost cannot be less than 0, the actual range would be [0,23475]

Ans b):

95% confidence interval for variable cost is given by

[16.53699 Critical Value*Standard Error]

For a t-statistic, critical value for 48 degrees of freedom and 95% confidence interval is 2.01

Hence the range of variable cost per square feet is = [16.53699 2.01*0.2133]

[16.108,16.965]

Ans C:

Minimum values of fixed cost and variable cost are 0 and 16.108 respectively

Maximum values of fixed cost and variable cost are 23475.8 and 16.965 respectively

Cost per square feet for 15000 sq ft lease would range in between

= [(0 + 16.108*15000/15000),(23475.8 + 16.965*15000/15000)]

= [16.108,18.53]

Ans D:

Total amount the company will pay for 15000 sq feet with 95% confidence is

= [(0 + 16.108*15000/15000),(23475.8 + 16.965*15000/15000)]

= [241623 to 277963]