I have a question that I have done a bit of...
just need checking
and if sumone can tell me how to do the rest...coz im confused
A chemist is interested in determining the weight loss y (in pounds) of a particular compound as a function of the amount of time x (in hours) the compound is exposed to the air.
A regression model y = βo + B1 + ε is fitted to the data observed, where ε is the random error term
having a standard deviation σ. An incomplete Minitab output is given below where C1 represents
the y variable and C2 represents the x variable.
The regression equation is
C1 = 1.44 + 0.720 C2
Predictor Coef SE Coef T P
Constant 1.440 1.346 1.07 0.3100
C2 0.7200 0.2398 ? ?
S = ??? R-Sq = ??? R-Sq(adj) = 42.2%
Analysis of Variance
Source DF SS MS F P
Regression 1 ??? 7.7760 ??? 0.013
Residual Error 10 8.6240 ???
Total 11 16.4000
Predicted Values for New Observations
New Obs Fit SE Fit 95.0% CI 95.0% PI
1 5.040 0.294 ( ??, ??) ( ??, ??)
Values of Predictors for New Observations
New Obs C2
(a) Calculate R2(i.e., R-Sq) — the proportion of the total variation in weight loss y observations that can be explained by x observations.
r2 = SSTO - SSE / SSTO
=16.4 - 8.624/16.4
(b) Calculate a 90% confidence interval for
1, the slope of the regression model.
b1 ± t* s.e. (b1)
= 0.72 ±1.81 x 0.2398
= 0.72 ± 0.434
= 0.286 to 1.154
(c) State and test the hypothesis about whether the slope
1 is different from 0. Use significance level
= 0.01 in the test. List H0 and Ha, the test statistic, the p-value and the conclusion.
Ho: β¹ ≠ 0
H1: β¹ = 0
T = ( b1 - 0 )/(s.e(b1)
(d) Find the fitted value of weight loss when the exposure time is 5 hours.
(e) Calculate a 95% confidence interval for the mean weight loss when the exposure time is 5
(f) Find the value of s — an estimate of — using the Minitab output supplied.
(g) Calculate a 95% prediction interval for the weight loss when the exposure time is 5 hours?