Question

Mr. Ali runs a gift shop in the Defense area, Karachi. He advertises weekly in the local newspapers and is considering increasing his advertising budget. Before doing so, he decides to evaluate the past effectiveness of these advertisements. Five weeks are sampled, and the advertising expenses (in PKR) and sales volume for each is shown in the Table 2. Develop a regression equation that would help Mr. Ali evaluate his advertising. FInd slope of this regression equaiton.

 

S.No.

Sales (PKR 100)

Advertising (PKR 100)

1.00

6.00

4.10

2.00

8.00

6.72

3.00

6.00

5.05

4.00

10.00

7.26

5.00

6.00

2.69

Answer 1

$\begin{matrix} X \space values(sales) &Y \space values(advertising ) \\ 6.00&4.10\\8.00&6.72\\6.00&5.05\\10.00&7.26\\6.00& 2.69\\\sum=36&\sum=25.82 \end{matrix}\\ Sum\space of\space X = 36, Sum \space of\space Y = 25.82,\\ Mean\space M_x = 7.2, Mean\space M_y = 5.164\\ --------------------------\\ \begin{matrix} X - Mx&Y - My& (X - Mx)2&(X - Mx)(Y - My)\\ -1.2&-1.064&1.44&1.2768\\ 0.8&1.556&0.64&1.2448\\ -1.2&-0.114&1.44&0.1368\\ 2.8&2.096&7.84&5.8688\\ -1.2&-2.474&1.44&2.9688\\ & & SS_X: 12.8&SP: 11.496\\ \end{matrix}\\ -------------------------- \\Sum\space of\space squares\space (SS_X)\space =\space 12.8\\ Sum\space of\space products\space (S_P)\space =\space 11.496\\ Regression\space Equation\space =\space ŷ\space =\space bX\space +\space a\\ b\space =\space \frac{SP}{SS_X}\space =\space 11.5/12.8\space =\space 0.89813\\ a\space =\space M_Y\space -\space b(M_X)\space =\space 5.16\space -\space (0.9*7.2)\space =\space -1.3025\\ ŷ\space =\space 0.89813X\space -\space 1.3025\\ --------------------------\\ slope \space of \space this \space regression \space equation.\\ value \space of\space coefficient\space of \space x\space in \space regression\space line\space is\space called\\ \space slope\space of\space regression \space line\\ hence\\ slope \space of \space this \space regression \space equation=0.89813\\$