CODEWITHSUNDEEP
rhypothesis-test
JRaanaas
JRaanaas

Reputation: 31

Hypothesis testing for | H0: B1=0 HA: B1=/=0 | in R

I want to test the hypothesis

H0: B1 = 0 HA: B1 =/= 0

with a 5% significance.

Is there a function for this kind of hypothesis testing?

What i currently got is:

                       Y                X
1                   1890             2075
2                   2790             2800
3                   1390             1450
4                    990             1175
5                   1290             1290
6                   1300             1400
7                   1890             1850
8                   1090             1070
9                   1290             1240
10                  2290             2480
11                  2690             3010
12                  1780             1850
13                  1490             1490
14                  1850             1910
15                  1850             1880
16                  1390             1420
17                  1560             1850
18                  2290             2260
19                   990             1175
20                  1290             1240

mod1 <- lm(d1$Y ~ d1$X)

Call:
lm(formula = d1$husdata.Salgssum ~ d1$husdata.Prisantydning)

Residuals:
    Min      1Q  Median      3Q     Max 
-129.48  -82.97  -29.40   93.02  217.85 

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)              13.75734   86.65964   0.159    0.876    
d1$husdata.Prisantydning  1.03743    0.04962  20.910 4.46e-14 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 113.9 on 18 degrees of freedom
Multiple R-squared:  0.9605,    Adjusted R-squared:  0.9583 
F-statistic: 437.2 on 1 and 18 DF,  p-value: 4.464e-14

I've found the critical value using the qt function, and have manually taking the estimation divided by std.error.

And then manually assess the the test value against the critical value.

qt(0.025, 18)

13.75734/86.65964

Upvotes: 0

Views: 1414

Answers (1)

Ricardo Semi&#227;o
Ricardo Semi&#227;o

Reputation: 4456

The coefficients table already has that answer!

Coefficients:
                         Estimate Std. Error t value Pr(>|t|)    
(Intercept)              13.75734   86.65964   0.159    0.876    
d1$husdata.Prisantydning  1.03743    0.04962  20.910 4.46e-14 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

The third column is the value of the test statistics of the null coefficient of the row = 0. The fourth is the probability of wrongly rejecting the null (p-value).

In your case, the p-value of the coefficient you're interested in is 4.46e-14 (very low, below 5%).

Upvotes: 1

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