For the data set below, complete parts (a) through (d) below. x 3, 4, 5, 7, 8 y
ID: 3229397 • Letter: F
Question
For the data set below, complete parts (a) through (d) below.
x 3, 4, 5, 7, 8
y 3, 5, 6, 13, 15
(a) Find the estimates of B0 and B1
B0 approx. = b0 = ? (round 3 decimals)
B1 approx. = b1 = ? (round 3 decimals)
(b) Compute the standard error, the point estimate for o
se = ? (round 4 decimals)
(c) Assuming the residuals are normally distributed, determine sb1
sb1 = ? (round 3 decimals)
(d) Assuming the residuals are normally distributed, test H0 : B1 = 0 vs H1 : B1 does not equal 0 at the a = 0.05 level of significance. Use the P-value approach.
The P-value for this test is ?
Make a statement regarding the null hypothesis and draw a conclusion for this test. Choose the correct answer below.
a) reject H0. There is sufficient evidence at the a=0.05 level of significance to conclude that a linear relation exists between x and y
b) reject H0. There is not sufficient evidence at the a=0.05 level of significance to conclude that a linear relation exists between x and y
c) Do not reject H0. There is not sufficient evidence at the a=0.05 level of significance to conclude that the linear relation exists between x and y
d) Do not reject H0. There is sufficient evidence at the a=0.05 level of significance to conclude that a linear relation exists between x and y
Explanation / Answer
(a)
B1 = 2.512
B0 = - 5.163
(b) Standard error , Point estimate = se = 0948
(c) Stanadard error of residual Sb1 = 0.229
(d) P - value for the test is = 0.002< 0.05 the significance level alpha = 0.05 so B1 is significant.
(Reject null hypothesis . There is sufficient evidence at alpha = 0.05 level of significane to conclude that a linear relation exists between x and y. Option a is correct.
SUMMARY OUTPUT Regression Statistics Multiple R 0.987796 R Square 0.97574 Adjusted R Square 0.967654 Standard Error 0.948275 Observations 5 ANOVA df SS MS F Significance F Regression 1 108.5023 108.5023 120.6621 0.001615 Residual 3 2.697674 0.899225 Total 4 111.2 Coefficients Standard Error t Stat P-value Lower 95% Intercept -5.16279 1.305506 -3.95463 0.028856 -9.31749 X 2.511628 0.228649 10.98463 0.001615 1.783964