Question

Cost and Customer Satisfaction

A researcher is interested whether there is a linear correlation between cost (in dollars) of internet service per month and customer satisfaction on a scale of 1 - 10 (with a 1 being extremely dissatisfied and 10 extremely satisfied). The researcher only includes internet service with similar download speed. The sample he collected is below.

Cost (x)	15	18	17	11	9	11	12	19	18	22
Satisfaction (y)	6	8	10	4	9	6	3	5	2	10

Find the best predicted value for the level of Customer Satisfaction given that the Cost is 13. Use a significance level of 0.05.
Round your answer to 1 decimal place, if needed.

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	152.00	63.00	163.60	74.10	24.40
mean	15.20	6.30	SSxx	SSyy	SSxy

Sample size,   n =   10      
here, x̅ = Σx / n=   15.200          
ȳ = Σy/n =   6.300          
SSxx =    Σ(x-x̅)² =    163.6000      
SSxy=   Σ(x-x̅)(y-ȳ) =   24.4      
              
estimated slope , ß1 = SSxy/SSxx =   24.4/163.6=   0.1491      
intercept,ß0 = y̅-ß1* x̄ =   6.3- (0.1491 )*15.2=   4.0330      
              
Regression line is, Ŷ=   4.033   + (   0.149   )*x

best Predicted Y at X=   13   is          
Ŷ=   4.03301   +   0.14914   *13=   5.972 ≈  6.0