Question

A scientist is studying the relationship between x = inches of annual rainfall and y = inches of shoreline erosion. One study reported the following data. Use the following information to solve the problem by hand, then use SPSS output to verify your answers. .

X         30        25        90        60        50        35       75        110      45        80

Y         0.3       0.2       5.0       3.0       2.0       0.5       4.0       6.0       1.5       4.0

a. What is the equation of the estimated regression line?

= ______________

b. Plot the data and graph the line. Does the line appear to provide 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 variance table

Source             DF                   SS                    MS                  F                      P

Regression       1                      37.938

Error                ____                _____              0.058               ____________

e) Is the simple linear regression model useful for predicting erosion from a given amount of rainfall?

f) What is the p-value?

g) A linear relationship ______________ exist between x and y.

h) The simple linear regression model ______________ useful for predicting erosion from a given amount of rainfall.

i) What is the coefficient of determination.(r-squared) or r?

j) Interpret the coefficient (r-squared) of determination.

Answer 1

USed excel to solve linear regression

IN excel use the data analysis tool then select data option -> regression-> input range of X and Y and click ok

ANswer (A)-regression line is Y=-1.736+0.0731*X

Answer (B) Yes, line appear to provide a good fit to the data points

Answer (C) when X=39

Y=-1.736+0.0731*X

Y=-1.736+0.0731*39=1.115

Answer (D)

Answer (E) Yes,simple linear regression model useful for predicting erosion from a given amount of rainfall

Answer(F) p value is 6E-09

Answer(I) R square= 0.988

ANswer(J) coefficient (r-squared) of determination =0.988 means 98.8% of the variance in shoreline erosion(Y)

explained by  annual rainfall(X).It measure the strength of realtionship between our model