An executive at a telecommunications company is interested in the relationship b

Question

An executive at a telecommunications company is interested in the relationship between an
individual’s income and their mobile phone usage. In particular, to help her in pricing and marketing
strategies, she is interested in ascertaining whether she can use an individual’s gross annual income
to predict how much time they will spend on making National Direct Calls from their mobile phone
per week.
She surveyed 12 mobile phone users and recorded their annual incomes and time (in minutes) spent
each week making National Direct Calls. The data are presented in sequence, according to gross
annual income.
Annual income ($000) 23 29 29 35 42 46 50 54 64 66 76 78
Weekly                        69 95 102 118 126 125 138 178 156 184 176 225
time on
National
Direct
Calls
(minutes)

(a) Develop a Regression model to predict mobile phone call times using annual income.
(10 marks)
(b) Calculate and interpret the coefficient of determination
(5 marks)
(c) Test the slope of the estimated regression to determine whether there is a significant positive
relationship between mobile phone call times and annual income. Use = 0.01. What conclusion
can you draw from this about the regression model you have developed?
(10 marks)

Please provide step by step instructions to help with my understanding. Thank you!

Explanation / Answer

a)

y^ = 30.9125 + 2.2315 * Income

b) R^2 = 0.8864

hence 88.64 % of variation in calls can be explained by income

c)

p-value for slope= 488 *10^(-6) << 0.01

hence we reject the null and conclude that there is a significant positive
relationship between mobile phone call times and annual income

SUMMARY OUTPUT Regression Statistics Multiple R 0.941506251 R Square 0.88643402 Adjusted R Square 0.875077422 Standard Error 15.64907915 Observations 12 ANOVA df SS MS F Significance F Regression 1 19115.06322 19115.06322 78.0545392 4.88631E-06 Residual 10 2448.936784 244.8936784 Total 11 21564 Coefficients Standard Error t Stat P-value Lower 95% Intercept 30.91246961 13.25422291 2.332273255 0.041887623 1.380220594 income 2.231503994 0.252579783 8.834848001 4.88631E-06 1.668721166

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