Question

#_Items_Sold	TV$	Conference$	JournalAd$
88,000	87,000	95,000	100,000
80,000	98,000	99,000	99,000
96,000	101,000	103,000	101,000
76,000	91,000	95,000	93,000
80,000	88,000	102,000	95,000
73,000	84,000	94,000	95,000
58,000	74,000	89,000	80,000
116,000	102,000	112,000	116,000
104,000	105,000	110,000	106,000
99,000	97,000	87,000	105,000
64,000	88,000	90,000	90,000
126,000	108,000	101,000	113,000
94,000	89,000	100,000	96,000
71,000	78,000	85,000	98,000
111,000	109,000	99,000	109,000
109,000	108,000	101,000	102,000
100,000	102,000	93,000	100,000
127,000	110,000	108,000	107,000
99,000	95,000	100,000	108,000
82,000	90,000	69,000	95,000
67,000	85,000	95,000	91,000
100,000	103,000	91,000	114,000
78,000	80,000	80,000	93,000
115,000	104,000	85,000	115,000
83,000	83,000	105,000	97,000
125,000	100,000	98,000	110,000
92,000	85,000	100,000	90,000
72,000	80,000	86,000	95,000

Part A - 10pts) Write down the regression equation for this problem.
Part B - 10pts) How good is this model? Explain your answer.
Part C - 10pts) Which promotional mix strategy below is predicted to produce most Items Sold (answer using all three input variables)?
	TV$	Conference	JournalAd
Strategy A)	80,000	70,000	80,000
Strategy B)	90,000	60,000	85,000
Strategy C)	55,000	85,000	100,000
Strategy D)	75,000	80,000	70,000
Strategy E)	95,000	70,000	65,000
Strategy F)	65,000	70,000	75,000
Part D - 10pts) Which variable is the most significant to the Target (Items Sold)?

Answer 1

1) Regression equation is Y = B₀ + B₁*X₁ +B₂*X₂ +B₃*X₃

So for this problem regression equation is JournalAd$ = -1.091e+05 + (9.081e-01 * TV) +

(8.722e-02* Conference) + (1.090e+00 * JournalAd)

and the formula of regression in R for this problem is lm(formula = `#_Items_Sold` ~ ., data = train1)

2) This is the good model because Multiple R-squared= 0.849, Adjusted R-squared = 0.8223, both values of R square and Adjusted R square are greater thatn 80%.

You can see the summery of this model below

summary(Model1)

Call:
lm(formula = `#_Items_Sold` ~ ., data = train1)

Residuals:
     Min       1Q   Median       3Q      Max 
-16402.8  -4576.6   -601.8   4974.3  17125.4 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -1.091e+05  2.391e+04  -4.565 0.000275 ***
TV           9.081e-01  2.950e-01   3.078 0.006818 ** 
Conference   8.722e-02  2.205e-01   0.395 0.697410    
JournalAd    1.090e+00  3.622e-01   3.010 0.007887 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8535 on 17 degrees of freedom
Multiple R-squared:  0.849,     Adjusted R-squared:  0.8223 
F-statistic: 31.86 on 3 and 17 DF,  p-value: 3.355e-07

3) according to this model the

Strategy A) value is 56853.4

Strategy B) value is 70512.2

Strategy C) value is 57259.2

Strategy D) value is 42285.1

Strategy E) value is 54124.9

Strategy F) value is 37781.9

4) TV and JournalAd are the most significant variables, you can see the results in summary, only TV and JournalAd have two stars.