Question

A computer manager needs to know how efficiency of her new computer program depends on the size of incoming data. Efficiency will be measured by the number of processed requests per hour. Applying the program to data sets of different sizes, she gets the following results:-

Data Size (gigabytes) (x)

6 7 7 8 10 10 15

Processed requests(y)

40 55 50 41 17 26 16

a. Find the equation of regression line

b. Interpret regression co-efficient and y intercept

c. Can we take Data Size as dependent variable if yes then how? If not then why? Explain.

d. Could this problem be studied using correlation if yes then how? If not then why? Explain.

Answer 1

solution a)

The regression equation is written as:

$$y=mx+c$$

Where $m$ and $c$ are the coefficients

Sum both sides of the equation:

$\sum y = m\sum x + c$ ........(equation 1)

Multiply equation 1 by $x$ to get equation 2

$\sum xy = m\sum x^2 + c\sum x$ ........(equation 2)

From data size $(x)$ we get:

$\sum x =63$

$\sum x^2 =623$

From processed requests $(y)$ we get:

$\sum y=245$

Multiplying $x$ and $y$ we get:

$\sum xy=1973$

Substituting these values in equations 1 and 2 we get:

$245 =63m+c$ ...... equation 1

$1973=623m+63c$ ....... equation 2

Solve the simultanious equations

From equation 1

$c=245-63m$

Substitute in equation 2

$1973=623m+63(245-63m)$

$13462=3346m$

$m=-4.02$

Hence

$1973= 623*(-4.02)+63c$

$63c=4477.46$

$c=71.07$

The regression equation is:

answer: $y=-4.02x +71.07$

solution b)

intercept, 71.07 is the expected number of processed requests when data size is 0 megabytes. The computer has atleast 71 processes running in any given hour when no data is provided.

Coefficient, -4.02 is the expected change in processed requests given a 1 gigabyte change in data size. Every new gigabyte of data introduced will reduce the number of requests the computer processes in a given hour atleast 4.

solution c)

YES. To calculate the model parameters, let data size be the $y$ variable and processed requests the $x$ variable. This model may answer the question, how much data to expect for a given frequency of requests per hour

solution d)

NO. Correlation is not a sufficient method of answering the manager's question.

It only shows the direction and degree the data appear to move relative to each other. It has no predictive power to explain the relationship