R programming question

a) Read the data file transform_data.txt from **the course website** into R, and make a scatterplot of y versus x. Clearly, the relationship is nonlinear and monotonic. I can tell you that a good transformation that linearizes the relationship is to take the sqrt of both and x and y. Make a scatterplot of the transformed data.

dat <- read.table(“http:// header=T) <<<< this is **the course website**

b) Perform regression on the transformed data, and overlay the regression line on the scatterplot of the transformed data in part a). Call the model lm.1 .

c) It appears that a good model for this data is sqrt(y) = alpha + beta sqrt(x). Using algebra alone (i.e. no R) show that this model is equivalent to the following model: y = alpha +beta_1 sqrt(x) + beta_2 x .

d) Fit a regression model of the form y = alpha + beta_1 sqrt(x) + beta_2 x to the data. Call it lm.2 .

e) To check that the two models (lm.1 and lm.2) are similar, make a scatterplot of their predictions. Just keep in mind that the second model predicts y, but the first model predicts sqrt(y)