For the data set shown below, complete parts (a) through (d) below. x = 20 30 40
ID: 3325187 • Letter: F
Question
For the data set shown below, complete parts (a) through (d) below. x = 20 30 40 50 60 y = 100 95 93 81 72
a) Use technology to find the estimates of B0 and B1
0 0 = ?? (Round to two decimal places as needed.)
1 b1= ?? (Round to two decimal places as needed.)
(b) Use technology to compute the standard error, the point estimate for .
se = ?? (Round to four decimal places as needed.)
(c) Assuming the residuals are normally distributed, use technology to determine sb1. sb1 = ?? (Round to four decimal places as needed.)
(d) Assuming the residuals are normally distributed, test H0: 1=0 versus H1: 10 at the =0.05 level of significance. Use the P-value approach.
Determine the P-value for this hypothesis test. P-value = ?? (Round to three decimal places as needed.)
Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 116.2 - 0.7 x
Sample size: 5
R (correlation coefficient) = -0.96812236
R-sq = 0.9372609
Estimate of error standard deviation: 3.3065591
Parameter estimates:
Analysis of variance table for regression model:
Hence,
a) bo = 116.20
b1 = -0.70
b) se = 3.3066
c) sb1 = 0.1046
d) P - value = 0.007
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 116.2 4.4362146 0 3 26.193503 0.0001 Slope -0.7 0.10456258 0 3 -6.6945555 0.0068