Question

Explain the coefficients and check the model assumptions of the table below.

Week	Sales	Direct Mail	Corrected
1	$121,230	9800	42047
2	$212,090	21200	9800
3	$99,980	561000	21200
4	$429,780	41300	56100
5	$496,370	26700	41300
6	$316,450	32100	26700
7	$286,980	52900	32100
8	$496,110	73100	52900
9	$389,080	69500	73100
10	$787,350	54400	69500
11	$446,310	8700	54400
12	$389,410	29900	8700
13	$420,040	24300	29900
14	$629,380	42300	24300
15	$419,370	82000	42300
16	$740,070	60200	82000
17	$498,730	48900	60200
18	$621,780	27900	48900
19	$317,620	37600	27900
20	$427,270	68621	37600

Answer 1

using excel>data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.651648
R Square	0.424645
Adjusted R Square	0.356956
Standard Error	144300.6
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	2.61E+11	1.31E+11	6.273495	0.009109
Residual	17	3.54E+11	2.08E+10
Total	19	6.15E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	251606.7	82281.74	3.057868	0.007118	78007.44	425206
Direct Mall	-0.41978	0.285255	-1.47159	0.159402	-1.02161	0.182057
Corrected	4.862824	1.661833	2.926181	0.009424	1.356663	8.368984

the regression equation is

Sales = 251606.7 -0,41978 Direct Mall +4.862824 Corrected

Explanation of coefficients

for every one unit increase in Direct Mall, there is 0.41978 decrease in sales

for every one unit increase in Corrected, there is a 4.862824 increase in sales.

Assumptions of normality is satisfied

Boxplot of Sales, Direct Mall, corrected 800000 700000 600000 500000 Data 400000 300000 200000 100000 Sales Direct Mall corrected