For the data set (1,3),(1,3),(4,6),(7,7),(9,10), find interval estimates (at a 9
ID: 3365607 • Letter: F
Question
For the data set
(1,3),(1,3),(4,6),(7,7),(9,10),
find interval estimates (at a 95.5% level) for a single observation and for the mean response of y corresponding to x=4.
Entered Answer Preview Result 1.350911136,14.6432065) (1.350911136, 14.6432065) incorrect (1.88672157,7.31327843) (1.88672157, 7.31327843) correct At least one of the answers above is NOT correct. (1 pt) For the data set find interval estimates (at a 95.5% level) for a single observation and for the mean response ofy corresponding to x = 4. Note: For each part below, your answer should use interval notation. Prediction Interval for Single Observation = (1.350911136, 14.6432065) Confidence Interval for Mean Response =Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 0.070588235 + 1.1323529 x
Sample size: 5
R (correlation coefficient) = 0.94711592
R-sq = 0.89702856
Estimate of error standard deviation: 1.8265472
Parameter estimates:
Analysis of variance table for regression model:
Predicted values:
Hence,
95.5% Prediction Interval for Single Observation = (-2.0461477, 11.246148)
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 0.070588235 1.2050978 0 3 0.058574695 0.957 Slope 1.1323529 0.22150138 0 3 5.1121711 0.0145