We want to know whether the diameter of sand grainsX on the

We want to know whether the diameter of sand grains(X) on the beach determines the beach slope(Y). We collected the data and performed the linear regression. The results are below.

Solution

(a) Yes ,Since if we perform a test H₀ : the reression of Y on X is linear H₁ : Not H₀ .

The test statistics is F,and p-value is 6.48 x 10^-5 << 0.05 [ we choose it in general ]

So we reject H₀ at 0.05 level of significance and conclude that X determines Y significantly.

(b) The goodness of fitting of the prediction formula is measured by R-square value,

Since it is 0.9104867 . and in general 0< R-square<1 ,and high value of R-square indicates high degree of goodness of fitting, this certainly implies that the prediction is good.

(c)The regression equation is Y= -2.475925 + 17.159369*x

(d) When x= 0.5 ,Y from the above equation is , Y\' = -2.475925 + 17.159369*0.5 = 6.10376 .

(e) The residual for the Y which is actually 5 , but 6.10376 when regressed from the Linear Regression equation is, = 5-6.10376 = -1.10376 .