Analyse de regression

a/

[pic 1]

I except to find a linear relationship between advertising and sales if I would fit a regression line to the data.

b/[pic 2]

Call:

lm(formula = Sales ~ Advert., data = exam)

Residuals:

    Min      1Q  Median      3Q     Max

-4.6794 -2.7869 -1.3811  0.6803 22.3206

Coefficients:

            Estimate Std. Error t value Pr(>|t|)    

(Intercept)  29.6269     4.8815   6.069 9.78e-06 ***

Advert.      -0.3246     0.4589  -0.707    0.488    

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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.836 on 18 degrees of freedom

Multiple R-squared:  0.02704,        Adjusted R-squared:  -0.02701

F-statistic: 0.5002 on 1 and 18 DF,  p-value: 0.4885

a=29.6269

b=-0.3246

std error of b = 0.4589

t value of b = -0.707

t value of b<2,so b is not significantly different from 0.

c/

[pic 3]

The residual is not normally distributed.

d/The large residual is due to the outliers in our data which correspond to the the week with opening hours during the evening. In order to get a more satisfactory model we need to remove the outliers from our data.

e/[pic 4]

Call:

lm(formula = Sales ~ Advert., data = exam1) 

Residuals:

    Min      1Q  Median      3Q     Max

-2.2500 -0.4375  0.0000  0.5000  1.7500

Coefficients:

            Estimate Std. Error t value Pr(>|t|)    

(Intercept)  21.1250     0.9548  22.124 5.72e-14 ***

Advert.       0.3750     0.0882   4.252 0.000538 ***

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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.054 on 17 degrees of freedom

Multiple R-squared:  0.5154,        Adjusted R-squared:  0.4869

F-statistic: 18.08 on 1 and 17 DF,  p-value: 0.0005379

a=21.125

b=0.3750

std error of b= 0.0882

t value of b = 4.252

t value of b <2, so b is significantly different from 0.

f/In part B,the outliers in our data affected dramatically  the regression mode. In the first model, b is not significantly different from 0 and the residual standard error is high.

After removing the outliers (week 12),the residual standard error diminished and b is  significantly different from 0,so our regression model is more adequate.

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