Consider a simple linear regression of potato yield tonsacre

Consider a simple linear regression of potato yield (tons/acre) on the amount of fertilizer used (cwt/acre).

Fertilizer   Yield

      0              8.4

      0              8.0

      2              12.0

      2               12.8

      5                44.2

      7                 100.6

      10               400.0

a. Create a scatter plot of the data. Does the plot indicate a linear association between potato yield and amount of fertilizer used?

b. Do a test for lack of linear fit at significance level .01. Comment on the findings.

All calculations must be done by hand without the use of statistical software.

Please show all work and steps for rating without using statistical software output.

Solution

It shows linear trend

b) H0: slope =0

Ha: slope not 0

Two tailed test at 0.01 level.