For the data set shown below, complete parts (a) through (d) below. X 3 4 5 7 8
ID: 3056974 • Letter: F
Question
For the data set shown below, complete parts (a) through (d) below.
X 3 4 5 7 8
Y 4 5 7 11 14
(a) Find the estimates of Bo and B1.
Bo=bo= _____ (Round to three decimal places as needed.)
B1=b1= ______(Round to four decimal places as needed.)
(b) Compute the standard error the point estimate for Se= ____
c) Assuming the residuals are normally distributed, determine Sb1=____ (Round to four decimal places as needed.)
(d) Assuming the residuals are normally distributed, test HoB1=0 versus H1:B1/=0 at the a=0.05 level of significance. Use the P-value approach. The P-value for this test is _____. (Round to three decimal places as needed.)
Make a statement regarding the null hypothesis and draw a conclusion for this test. Choose the correct answer below.
A. Reject Ho. 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 Ho. 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 Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y.
D. Do not reject Ho. 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
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = -2.6627907 + 2.0116279 x
Sample size: 5
R (correlation coefficient) = 0.99150577
R-sq = 0.98308369
Estimate of error standard deviation: 0.63184239
Parameter estimates:
Analysis of variance table for regression model:
Hence,
a) b0 = -2.663
b1 = 2.0116
b) se = 0.6318
c) sb1 = 0.1524
d) P - value = 0.001
e) Reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y. Option A is correct.
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -2.6627907 0.86986796 0 3 -3.0611435 0.0549 Slope 2.0116279 0.15235073 0 3 13.203927 0.0009