Question

TREND
Billed Charge	Visit Time (Minutes)
$               13,924.00	220
$                  4,956.00	180
$                  8,496.00	165
$               12,036.00	200
$                  4,956.00	173
$               10,384.00	235
$               12,980.00	231
$               10,148.00	215
$                  8,024.00	170
$               12,508.00	295
$               11,328.00	198
$                  9,440.00	145
$               13,452.00	216
$               10,620.00	199
$               10,384.00	240
$                  5,664.00	124
$                  7,316.00	200
$               10,148.00	215
$                  5,900.00	184
$                  7,788.00	165
TREND
Computer the trend for the new visit times in minutes.
Visit Times (min)
300
305
310
320
Now that you have determined the answer, it is time to provide a 1 or 2 sentence
write up of your answer. In statistics, it is important that you not only get the correct
mathematical answer, but that you become comfortable writing up your results in
a manner that is easily understood by the reader/audience.

Answer 1

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
220	13924	462.25	19372321.96	94630.10
180	4956	342.25	20853835.56	84482.10
165	8496	1122.25	1053907.56	34391.10
200	12036	2.25	6317179.56	3770.10
173	4956	650.25	20853835.56	116448.30
235	10384	1332.25	742009.96	31441.10
231	12980	1056.25	11953614.76	112365.50
215	10148	272.25	391125.16	10319.10
170	8024	812.25	2245801.96	42710.10
295	12508	9312.25	8912613.16	288091.10
198	11328	0.25	3259469.16	-902.70
145	9440	2862.25	6822.76	4419.10
216	13452	306.25	15440184.36	68764.50
199	10620	0.25	1204286.76	548.70
240	10384	1722.25	742009.96	35748.10
124	5664	5550.25	14888793.96	287465.70
200	7316	2.25	4869083.56	-3309.90
215	10148	272.25	391125.16	10319.10
184	5900	210.25	13123230.76	52527.70
165	7788	1122.25	3008837.16	58109.10

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	3970	190452	27413	149630088.8	1332338.00
mean	198.50	9522.60	SSxx	SSyy	SSxy

sample size ,   n =   20          
here, x̅ = Σx / n=   198.50   ,     ȳ = Σy/n =   9522.60  
                  
SSxx =    Σ(x-x̅)² =    27413.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   1332338.0          
                  
estimated slope , ß1 = SSxy/SSxx =   1332338.0   /   27413.000   =   48.6024
                  
intercept,   ß0 = y̅-ß1* x̄ =   -124.9794          
                  
so, regression line is   Ŷ =   -124.9794   +   48.6024   *x

......

For x(new visit time) = 300

Y(New billed charge) = -124.9794   +   48.6024   *300 = 14455.75

Similarly we can calculate for others value.

New Visit Time	New Billed Charge
300	$14,455.75
305	$14,698.76
310	$14,941.77
320	$15,427.79

We have first created the relationship/equation between two variable(dependent and independent) using trend/regression analysis. Using that trend equation we have predicted the dependent variable based on independent variable.