Question

An executive at a telecommunications company is interested in the relationship between an individual’s income and their mobile phone usage. He surveyed 10 mobile-phone users and recorded their annual incomes and time (in minutes) spent each week making national direct calls. The data is presented in sequence according to gross annual income.  

 

Individual Annual income (000) National direct calls (minutes) 1 23 69 2 29 95 3 35 118 4 42 136 5 46 125 6 50 138 7 64 166 8 66 184 9 76 170 10 78 225 

  

 

a. Construct a scatter plot of the data above. (3 marks)  

 

b. Develop a least squares regression line to predict the direct calls in minutes based on annual income. (10 marks)  

 

c. What would be the predicted duration of direct call in minutes for an income of $48000? (3 marks) 

 

d. What is the error value for an income of $76000? (4 marks) 

Answer 1

a) Scatter plot:

b) Regression analysis:

Regression equation:

$y ′ =6776.14685X+1529.3779$

c) When income is $43000, the predicted direct calls:

Using the regression equation:

$y′=6776.14685X+1529.3779 \\X = \$43000\\Y ′ =6776.14685\times43000+1529.37879 \\Y ′ =277185843.92879$

d) Error formula:$S e ​ =∑e i 2 ​ =∑(Y−Y ′ ) 2 $

Y' when X = $76000$Y ′ =6776.14685∗76000+1529.37879 \\Y ′ =514988689.97879 \\∑e 2 =(45574.3333−514988689.97879) 2 =(−277140269.59549) 2 \\=7.68067290E+16$