Answer:
a).
The estimated regression line is
y = 1.2405+0.1666*x
b).
95% CI for intercept = (-0.482, 2.963)
95% CI for slope= (0.083, 0.250).
c).
d).
To test the significance of the model, calculated F=17.69, P=0.0005 which is < 0.05 level of significance. Ho is rejected. The linear relation is significant.
e).
when pollution index is 10.7,
predicted y value is = 3.0226
95% prediction interval for this mortality rate is (0.9538 , 5.0914 )
Excel Addon Megastat used.
Menu used: correlation/Regression ---- Regression Analysis
Regression Analysis |
|||||||
r² |
0.4957 |
n |
20 |
||||
r |
0.7041 |
k |
1 |
||||
Std. Error of Estimate |
0.8898 |
Dep. Var. |
y |
||||
Regression output |
confidence interval |
||||||
variables |
coefficients |
std. error |
t (df=18) |
p-value |
95% lower |
95% upper |
|
Intercept |
a = |
1.2405 |
0.820 |
1.513 |
.1477 |
-0.482 |
2.963 |
x |
b = |
0.1666 |
0.040 |
4.206 |
.0005 |
0.083 |
0.250 |
ANOVA table |
|||||||
Source |
SS |
df |
MS |
F |
p-value |
||
Regression |
14.009 |
1 |
14.009 |
17.69 |
.0005 |
||
Residual |
14.252 |
18 |
0.792 |
||||
Total |
28.261 |
19 |
|||||
Predicted values for: y |
|||||||
95% Confidence Interval |
95% Prediction Interval |
||||||
x |
Predicted |
lower |
upper |
lower |
upper |
Leverage |
|
10.7 |
3.0226 |
2.1366 |
3.9085 |
0.9538 |
5.0914 |
0.225 |
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