Question

Research and development section of ABC company is interested to study whether number of salesmen significantly affect the sales of the number of bottles of a particular type of soft dring offered by many companies in the market. Below is the randomly collected of 9 companies data by the R&D section of ABC company:

Salesmen	15	30	35	30	45	42	65	30	45
No. of bottles sold	330	600	700	650	845	758	954	300	754

1. What will be sample regression line for this regression study?
2. Estimate the regression line and interpret its estimates.
3. Test the hypothesis whether effect of the number of salesmen on number of bottles sold is significant.
4. Interpret the error term in the regression model.
5. Using the estimated regression line, estimate the number of bottles sold if a random company uses 50 salesmen to sell the bottles.

Answer:

Answer 1

Interpretation -

b0 : Y-intercept, can be interpreted as the value you would predict for Y if both X1 = 0 and X2 = 0.

b1 : represents the difference in the predicted value of Y for each one-unit difference in X1, if X2 remains constant. i.e.

One unit change in independant variable will change the dependant variable by 13.4795

3) Hypothesis :

b1 = 0 vs b1 != 0

Test Statistic = b1 / se = 13.4795 / 2.9757 = 4.5298

P value = 0.0027

Decision - reject H0 as p value < 0.05

Conclusion - b1 is non zero.

4) Error term - it refers to the sum of the deviations within the regression line, which provides an explanation for the difference between the theoretical value of the model and the actual observed results.

5) if salesmen = 50 then no. of bottles sold will be

= 149.8240 + 13.4795 * 50 = 824

PL?☺️