The iPhone six has been out for few years now and a lot of data has been collect
ID: 3062922 • Letter: T
Question
The iPhone six has been out for few years now and a lot of data has been collected. A marketing firm wants to model the price (p) of an iPhone six and Weekly Demand (s). Below is a table of data that have been collected. Price-p, (S) 150 170 190 210 230 250 Weekly Demand = s, (1 ,000s) 217 208 191 190 183 Round answers to 4 decimal places. a) Find the correlation coefficient, be careful with the sign. b) Perform a hypothesis test to see if the correlation is statistically significant. What is the p-value? c) Is the correlation statistically significant at the 0.01 significance level? Select an answer d) Find the linear model that best fits this data using regression and enter the model below. Be careful what letterts) you use Preview c) What does the model predict will be the weekly demand if the price of an iPhone six is s175? thousand d) According to the model at what should the price be set in order to have a weekly demand of 195,500 iPhone sixes? Hint: Set weekly demand at 195.5 and solve for price. Round your answer to the nearest dollarExplanation / Answer
Result:
a).
correlation r= -0.9784
b). P= 0.0007
c).
calculated p=0.0007 < 0.01 level. Correlation is significant.
d).
s=280.7619-0.4371*p
e).
when p=175,
predicted s =280.7619-0.4371*175
= 204.27
f)
195.5=280.7619-0.4371*p
p=195
Regression Analysis
r²
0.9573
n
6
r
-0.9784
k
1
Std. Error
3.8625
Dep. Var.
demand
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,337.6571
1
1,337.6571
89.66
.0007
Residual
59.6762
4
14.9190
Total
1,397.3333
5
Regression output
confidence interval
variables
coefficients
std. error
t (df=4)
p-value
95% lower
95% upper
Intercept
280.7619
9.3669
29.974
7.38E-06
254.7553
306.7685
price
-0.4371
0.0462
-9.469
.0007
-0.5653
-0.3090
Predicted values for: demand
95% Confidence Interval
95% Prediction Interval
price
Predicted
lower
upper
lower
upper
Leverage
175
204.262
198.836
209.687
192.244
216.280
0.256
Regression Analysis
r²
0.9573
n
6
r
-0.9784
k
1
Std. Error
3.8625
Dep. Var.
demand
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,337.6571
1
1,337.6571
89.66
.0007
Residual
59.6762
4
14.9190
Total
1,397.3333
5
Regression output
confidence interval
variables
coefficients
std. error
t (df=4)
p-value
95% lower
95% upper
Intercept
280.7619
9.3669
29.974
7.38E-06
254.7553
306.7685
price
-0.4371
0.0462
-9.469
.0007
-0.5653
-0.3090
Predicted values for: demand
95% Confidence Interval
95% Prediction Interval
price
Predicted
lower
upper
lower
upper
Leverage
175
204.262
198.836
209.687
192.244
216.280
0.256
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