A scientist is studying the relationship between x =inches of annual rainfall and y = inches of shorelineerosion. One study reported the following data. Use the followinginformation to solve the problem by hand, then use SPSS output toverify your answers. .
XÂ Â Â Â Â Â Â Â 30Â Â Â Â Â Â Â 25Â Â Â Â Â Â Â 90Â Â Â Â Â Â Â 60Â Â Â Â Â Â Â 50Â Â Â Â Â Â Â 35Â Â Â Â Â Â 75Â Â Â Â Â Â Â 110Â Â Â Â Â 45Â Â Â Â Â Â Â 80
YÂ Â Â Â Â Â Â Â 0.3Â Â Â Â Â Â 0.2Â Â Â Â Â Â 5.0Â Â Â Â Â Â 3.0Â Â Â Â Â Â 2.0Â Â Â Â Â Â 0.5Â Â Â Â Â Â 4.0Â Â Â Â Â Â 6.0Â Â Â Â Â Â 1.5Â Â Â Â Â Â 4.0
a. What is the equation of the estimated regression line?
= ______________
b. Plot the data and graph the line. Does the line appear toprovide a good fit to the data points?
c. Use the least-squares line to predict the value of y when x=39
d. Fill in the missing entries in the SPSS analysis of variancetable
Source            DF                  SS                   MS                 F                     P
Regression      1                     37.938
Error               ____               _____             0.058              ____________
e) Is the simple linear regression model useful for predictingerosion from a given amount of rainfall?
f) What is the p-value?
g) A linear relationship ______________ exist between x andy.
h) The simple linear regression model ______________ useful forpredicting erosion from a given amount of rainfall.
i) What is the coefficient of determination.(r-squared) orr?
j) Interpret the coefficient (r-squared) of determination.
