Question

b) Interpret the coefficients in the estimated regression model of Sales on Csales. c) Before estimating the model, the manager claimed that for every 1 million increase in Csales, Sales go down by 2 million. Is there evidence from the estimated model that she was not correct? Answer by constructing an appropriate 95% confidence interval. d) What is the correlation between Sales and Csales?

Region	Sales	Advertising	Promotions	Csales
Selkirk	101.8	1.3	0.2	20.4		Csales=main competitor's sales
Susquehanna	44.4	0.7	0.2	30.5		Sales=sales of company's Nature -Bar
Kittery	108.3	1.4	0.3	24.6
Acton	85.1	0.5	0.4	19.6
Finger Lakes	77.1	0.5	0.6	25.5
Berkshires	158.7	1.9	0.4	21.7
Central	180.4	1.2	1	6.8		all variables are in millions of dollars
Providence	64.2	0.4	0.4	12.6
Nashua	74.6	0.6	0.5	31.3
Dunster	143.4	1.3	0.6	18.6
Endicott	120.6	1.6	0.8	19.9
Five-Towns	69.7	1	0.3	25.6
Waldeboro	67.8	0.8	0.2	27.4
Jackson	106.7	0.6	0.5	24.3
Stowe	119.6	1.1	0.3	13.7

Answer 1

Here I have solved this question by using MINITAB.

(Stat -> Regression-> Response Y -> Predictor X-> OK)

Let ,    Y – Sales

            X - Csales

Correlations: y, x

Pearson correlation of y and x = -0.625

Here Sales and Csales are negatively correlated.

Interpretation of coefficient : For every 1 million increase in csales , sales goes down by 3.54 million.

Regression Analysis: y versus x

The regression equation is  y = 178 - 3.54 x

Predictor    Coef SE Coef      T      P

Constant   177.70    27.59   6.44 0.000

x          -3.545    1.228 -2.89 0.013

Inverse Cumulative Distribution Function

Student's t distribution with 13 DF

P( X <= x )        x

      0.975 2.16037

To check claim of manager :

95 % confidence interval :

(β₁ – t_((n-2),α/2)*S.E(β₁)   , β₁+ t_((n-2),α/2)*S.E(β₁))

(-3.545 – t_((13),α/2)*1.228   , -3.545+ t_((13),α/2)*1.228)

(-3.545 – 2.16037*1.228   , -3.545+ 2.16037*1.228)

(-6.1979 , -0.8921)

Conclusion : β1=0 does not lies in above interval . Hence, manager claim was not correct.