Answer to Question #199706 in Statistics and Probability for kauser

Question

Apply Regression Model and find out b0 and b1, additionally, try to find out Karl

Person’s Correlation Coefficient. Write the interpretation covering correlation and

estimated quantities in regression analysis (b0 and b1 only).

The below given table show the Region wise sales of Govind Chips, the data is

collected for 26 districts of Gujarat. Reference period of this data is 2019-2020.

ales figures are in lakhs and spending in advertisement is also given in Lakhs.

District Sales(00,000' INR) Amount spending in Advertisement(00,000'INR)

Kachchh 40 3.6

Banas Kantha 19 2.1

Patan 20 2.2

Mahesana 30 2.5

Sabar Kantha 27 2.3

Gandhinagar 50 6

Ahmadabad 49 5

Surendranagar 26 2.3

Rajkot 45 3.7

Jamnagar 48 3.8

Porbandar 14 1.7

Junagadh 44 3.6

Amreli 32 2.8

Bhavnagar 29 2.3

Anand 33 3

Kheda 14 1.8

Panch Mahals 45 3.9

Dohad 13 1.5

Vadodara 49 4.5

Narmada 25 2

Bharuch 39 3.5

The Dangs 11 1

Navsari 18 2

Valsad 30 2.9

Surat 48 4

Tapi 17 1.9

Answer 1

Regression Model:

$y=b_1x+b_0$

$b_1=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-(\sum x)^2}$

$b_0=\frac{n\sum y\sum x^2-\sum x\sum xy}{n\sum x^2-(\sum x)^2}$

x is Sales, y is Advertisement.

Using online calculator www.socscistatistics.com, we get:

$y=0.08x+0.28$

with slope=0.08 (rate of increasing of Advertisement respect to Sales) and

y-intercept=0.28 (value of Advertisement for Sales=0)

Correlation Coefficient:

$r=\frac{\sum (x_i-\overline{x})(y_i-\overline{y})}{\sqrt{\sum (x_i-\overline{x})^2\sum(y_i-\overline{y})^2}}$

Using online calculator www.socscistatistics.com, we get:

$r=0.936$

This is a strong positive correlation, which means that high x (Sales) variable scores go with high y (Advertisement) variable scores (and vice versa).