Question

Station	Square Footage	Turnout Time (in minutes)	Area Squared	Time Squared	Area * Time
31	3842	1.82	14760964	3.3124	6992.44
32	11572	1.86	133911184	3.4596	21523.92
33	6802	2.13	46267204	4.5369	14488.26
34	18500	2.37	342250000	5.6169	43845
35	19232	1.92	369869824	3.6864	36925.44
36	4500	2.33	20250000	5.4289	10485
37	6700	2	44890000	4	13400
38	3093	2.02	9566649	4.0804	6247.86
39	9229	2.22	85174441	4.9284	20488.38
40	6094	2.42	37136836	5.8564	14747.48
41	15130	2.44	228916900	5.9536	36917.2
42	7523	2.22	56595529	4.9284	16701.06
43	15000	3.18	225000000	10.1124	47700
44	9000	2.18	81000000	4.7524	19620
45	9647	2.35	93064609	5.5225	22670.45
46	15130	2.5	228916900	6.25	37825
Sum	160994	35.96	2017571040	82.4256	370577.49
Mean (2 point)	403620545.98			Correlation Coefficient (2 point)	Coefficient of Determination (2 point)
SD (2 point)	902225767.07			0.3460507
What is the Dependent Variable (2 point)?
Turnout Time
What is the Independent Variable (2 point)?
Square Foot
Place a scatterplot of the data below (4 points).  Show the trendline as well. Remember to include titles and labels.
What does this data tell you about the relationship (4 points)?
Positive trend but weak relationship /correlation
State the equation of the least-squares regression line (2 point).
y= a+bx b= N∑xy-(∑x)(∑y)          N∑xr-(∑x)v
Identify and interpret the slope (4 points).
b= 0.0000219
Identify and interpret the intercept (4 points).
Intercept a= y-bx(x) a=2.02796 x=25000 y^1= 2.575868
If appropriate, use the least-squares regression equation to predict the turnout time for a 12,000 square foot fire station (4 points).
y=2.02796+0.0000219*x x= 12000 y^1= 2.290957
If appropriate, use the least-squares regression equation to predict the turnout time for a 25,000 square foot fire station (4 points).
x=25000 y^1= 2.575868
Obtain the residual plot and analyze the output (4 points).
Plot
Analysis

Answer 1

Turnout Time	Fitted	Residual
1.82	2.11073	-0.2907256
1.86	2.2807	-0.420700659
2.13	2.17581	-0.045813074
2.37	2.43304	-0.063040531
1.92	2.44914	-0.529136487
2.33	2.12519	0.204805631
2	2.17357	-0.173570195
2.02	2.09426	-0.07425583
2.22	2.22918	-0.009180405
2.42	2.16024	0.259755146
2.44	2.35894	0.081062438
2.22	2.19167	0.028332849
3.18	2.35608	0.82392101
2.18	2.22414	-0.044144921
2.35	2.23837	0.111628188
2.5	2.35894	0.141062438

From the residual VS order plot, we know that residual has a trend. Hence, it violates the assumption of randomness on model error.