Suppose an environmental agency would like to investigate therelationship between the engine size of​ sedans, x, and the milesper gallon​ (MPG), y, they get. The accompanying table shows theengine size in cubic liters and rated miles per gallon for aselection of sedans. The regression line for the data is yhat=36.7920−4.1547x.
Use this information to complete the parts below.
Engine Size  MPG
2.4 27
2.1 31
2.3 26
3.4 22
3.5 24
2.2 28
2.2 24
2.1 29
3.9 20
a) Calculate the coefficient of determination. R2=?(Round to three decimal places as​ needed.)
b) Using α=0.05​, test the significance of the populationcoefficient of determination.
Determine the null and alternative hypotheses.
c) The​ F-test statistic is? ​(Round to two decimal placesas​needed.)
d) the p-value is? ​(Round to three decimal placesas​needed.)
e) Construct a​ 95% confidence interval for the average MPG of a2.5​-cubic liter engine.
UCL= ? ​(Round to two decimal places as​ needed.)
LCL= ​? (Round to two decimal places as​ needed.)
f) Construct a​ 95% prediction interval for the MPG of a2.5​-cubic liter engine.
UPL= ? ​(Round to two decimal places as​ needed.)
LPL= ? ​(Round to two decimal places as​ needed.)
