Use the table “Food and Beverage Sales for Paul’s Pizzeria” to answer the questi
ID: 2453324 • Letter: U
Question
Use the table “Food and Beverage Sales for Paul’s Pizzeria” to answer the questions below.
Food and Beverage Sales for Paul’s Pizzeria Restaurant
($000s)
Month
First Year
Second Year
January
55
60
February
53
54
March
53
56
April
63
44
May
64
44
June
54
34
July
33
36
August
35
37
September
25
28
October
30
30
November
35
38
December
54
52
Part (a): Calculate the regression line and forecast sales for March of Year 3.
Part (b): Calculate the seasonal forecast of sales for March of Year 3.
Part (c): Which forecast do you think is most accurate and why?
Food and Beverage Sales for Paul’s Pizzeria Restaurant
($000s)
Month
First Year
Second Year
January
55
60
February
53
54
March
53
56
April
63
44
May
64
44
June
54
34
July
33
36
August
35
37
September
25
28
October
30
30
November
35
38
December
54
52
Explanation / Answer
first year = x
second year = y
x sum=> 55+53+53+63+64+54+33+35+25+30+35+54 =>554
y sum => 60+54+56+44+44+34+36+37+28+30+38+52 => 513
xy sum => 55*60+53*54+53*56+and so on.... => 24775
x2sum => 552+532+532+632+ and so on... => 27604
y2sum => 602+542+562+442+ and so on... =>23177
N= 12
The best form for our line is slope-intercept form, which looks like y = ax + b. Therefore, it is only necessary to compute m and b to determine the best fit line. Those values can be computed by the following equations:
a = (Nxysum) - (xsumysum) / (Nx2sum) - (xsumxsum)
b = (x2sumysum) - (xsumxysum) / (Nx2sum) - (xsumxsum)
a=> (12*24775)-(554*513) / (12*27604)-(554*554)
=> 297300-284202 / 331248 -306916
=> 0.5383
b=> (27604*513)-(554*24775) / (12*27604)-(554*554)
=> 14160852 - 13725350 / 331248 - 306916
17.8972
y= ax+b
y=0.5383x+17.8972
Regression line => y=0.5383x+17.8972
seasonlal forecast of sales for year 3 is 54.5
Regression line is better to solve, as it forecast as per graph takin into consideration all the aspects
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