Run a multiple regression using data from above. A) Interpret the P-value from t

Question

Run a multiple regression using data from above.

A) Interpret the P-value from the multiple regression

B) interpret the T-stat from the multiple regression

C) Run a multiple regression using only Nonfood sales and store size instead of all three independent variables. Which model do you prefer? Why?

Food Sales Nonfood Sales Store Size Profit Supermarket Number (tens of thousands (tens of thousands (thousands of (thousands of dollars) 19 square feet) ?? 35 of dollars) of dollars) 20 15 17 305 130 189 175 101 269 421 195 282 203 35 98 83 76 93 27 16 28 46 56 12 40 32 16 27 35 57 31 92 10 23

Explanation / Answer

> y <- c(20,15,17,9,16,27,35,7,22,23);y
[1] 20 15 17 9 16 27 35 7 22 23
> x1 <- c(305 , 130 , 189 , 175, 101, 269, 421, 195, 282, 203);x1
[1] 305 130 189 175 101 269 421 195 282 203
> x2 <- c(35,98,83,76,93,77,44,57,31,92);x2
[1] 35 98 83 76 93 77 44 57 31 92
> x3 <- c(35,22,27,16,28,46,56,12,40,32);x3
[1] 35 22 27 16 28 46 56 12 40 32
> dat <- data.frame(y,x1,x2,x3);dat
y x1 x2 x3
1 20 305 35 35
2 15 130 98 22
3 17 189 83 27
4 9 175 76 16
5 16 101 93 28
6 27 269 77 46
7 35 421 44 56
8 7 195 57 12
9 22 282 31 40
10 23 203 92 32
> regressor <- lm(y ~ . ,data = dat)
> summary(regressor)

Call:
lm(formula = y ~ ., data = dat)

Residuals:
Min 1Q Median 3Q Max
-1.7111 -0.2484 0.1024 0.4532 1.9631

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) -10.17024 3.47313 -2.928 0.026346 *  
x1 0.02704 0.01204 2.246 0.065847 .  
x2 0.09705 0.03015 3.219 0.018153 *  
x3 0.52468 0.05916 8.869 0.000114 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.25 on 6 degrees of freedom
Multiple R-squared: 0.9849, Adjusted R-squared: 0.9773
F-statistic: 130.1 on 3 and 6 DF, p-value: 7.555e-06

> regressor1 <- lm(y ~ x2+x3 , data = dat)
> summary(regressor1)

c)Call:
lm(formula = y ~ x2 + x3, data = dat)

Residuals:
Min 1Q Median 3Q Max
-1.9971 -0.8618 0.0674 0.6691 2.5109

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) -3.75836 2.48325 -1.513 0.174   
x2 0.04311 0.02288 1.884 0.102   
x3 0.63378 0.04238 14.953 1.44e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.57 on 7 degrees of freedom
Multiple R-squared: 0.9721, Adjusted R-squared: 0.9642
F-statistic: 122.1 on 2 and 7 DF, p-value: 3.615e-06

a)the p- value is 7.555e-06

b)values of t-stat is

-2.928
x1 2.246 .  
x2 3.219  
x3 8.869

c) From c it is seen that the p-value in new model is less than the previous model so this model is more effective than previous one . This process is called backward elimination.

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