Question

The Pepsi Corporation wants to explore the relationship between the daily temperature in California and the quantity of soft drinks that it sells at Dadger’s Baseball Stadium. The average daily temperature for 12 randomly selected days and the quantity of soft drinks sold on each of these days are given below:

Average Daily Temperature

            70
            75
            80
            90
            93
            98
            72
            75
            75
            80
            90
            95

Quantity Sold (thousands)

           30
           28
           40
           52
           57
           54
           27
           38
           32
           46
           49
           51

Construct a 90% confidence interval for the quantity of soft drinks sold when the temperature is 750.

Answer 1

Average Daily Temperature	Quantity Sold (Thousands)
70	30
75	28
80	40
90	52
93	57
98	54
72	27
75	38
75	32
80	46
90	49
95	51

Based on the above data we run a regression with confidence interval as 90%. The regression outsput is shown below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.930913559
R Square	0.866600054
Adjusted R Square	0.85326006
Standard Error	4.164371857
Observations	12
	azq
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1126.58007	1126.58007	64.96254915	1.10291E-05
Residual	10	173.4199297	17.34199297
Total	11	1300
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 90.0%	Upper 90.0%
Intercept	-43.05885111	10.62154192	-4.053917167	0.002309003	-66.72512133	-19.3925809	-62.3099829	-23.80771933
Average Daily Temperature	1.027901524	0.127532238	8.05993481	1.10291E-05	0.74374199	1.312061058	0.796754301	1.259048747

So the regression equation is given by

Y = 1.027901524*X - 43.05885111

Here Y = Quantity sold in thousands

X = Average Daily Temperature

Based on the above equation When X = 75

We have Y = .027901524*75 - 43.05885111

= 34

So Quantity sold in thousands is 34