c..assuming the residuals are normally distributed determine Sb1 ? d. assuming t
ID: 3369474 • Letter: C
Question
c..assuming the residuals are normally distributed determine Sb1 ? d. assuming the residuals are normally distributed use the p value aporoach. pvalue test is ? make a statement regarding the null hypothesis and draw a conclusion from the test.
Southern New Hamp HomeStudents ?? https://www.math MAT-240-T5257 Applied Statistics 18EW5 MyStatLab: Homework: 7-2 Score: 2.67 of 8 pts 14.1.5-T For the data set shown below, complete parts (a) through (d) below. M1 3 4 12 14 y 3 67 13 14 (a) Find the estimates of po and B. Po bo3.581 (Round to three decimal places as needed ) Pib2256 (Round to three decimal places as needed ) (b) Compute the standard error, the point estimate for ? Round to four decimal places as needed )Explanation / Answer
Here R-code for above problem is,
y=c(3,6,7,13,14)
x=c(3,4,5,7,8)
d=data.frame(y,x)
l=lm(y~x);l
a=aov(y~x,d)
summary(l)
And the output is:
> l=lm(y~x);l
Call:
lm(formula = y ~ x)
Coefficients:
(Intercept) x
-3.581 2.256
> a=aov(y~x,d)
> summary(l)
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5
-0.1860 0.5581 -0.6977 0.7907 -0.4651
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.5814 1.0285 -3.482 0.0400 *
x 2.2558 0.1801 12.523 0.0011 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.7471 on 3 degrees of freedom
Multiple R-squared: 0.9812, Adjusted R-squared: 0.975
F-statistic: 156.8 on 1 and 3 DF, p-value: 0.001098
a) Here we are getting:
b0 = -3.581
b1 = 2.256
b) Estimate of Residual standard error: 0.7471 on 3 degrees of freedom.
c) Also standerd error of coefficient of X= Sb1 = 0.1801
d) Here p-value for given testing of model is less than 0.05. Thus we reject null hypothesis as model is significant.
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