Here's my situation:
The equation for a simple linear regression model (below) was calculated and the summary output for the model was produced (below). The task is to calculate all equations by hand; however, for the sake of other users, I incorporated the data in R format too.
Linear Regression Model:
y = -0.76 + 1.21x
Data in R format
structure(list(x = c(74L, 77L, 79L, 84L, 95L, 98L, 112L, 120L, 128L, 129L, 132L, 135L, 136L, 147L, 148L, 149L, 150L, 153L, 159L, 161L, 161L, 163L, 197L), y = c(85L, 91L, 95L, 104L, 110L, 107L, 134L, 146L, 169L, 156L, 165L, 166L, 169L, 172L, 173L, 189L, 182L, 180L, 195L, 186L, 196L, 195L, 231L)), .Names = c("x", "y"), class = "data.frame", row.names = c(NA, -23L))
Based on the linear regression model fitted, calculate estimates and 95% prediction intervals for the weight after 35 days for larvae weighing 128 mg initially and 200 mg initially. State which of the prediction intervals for x = 128 and x = 200 is the wider, and explain why it is wider.
I have attempted to calculate the prediction intervals for when x = 128 mg and x = 200 mg by hand, which will be used for further data analysis; however, my answers appear to be rather spurious. My main concern is that I feeling unsure about weather I plugged the correct values from the model summary output (below) into the prediction interval equations (below).
More specifically, I am unsure whether I should be multiplying either the standard error prediction or the standard deviation of the x-value with the t-value based on the 95 % prediction level with 21 degrees of freedom and what does the notation Sxx mean?
- What does Sxx stand for?
- Do you multiply the t-value with the standard prediction value or the standard deviation for the x-values?
- Does the notation for S in the prediction equation stand for standard prediction error or the standard deviation for the x values
- Which interval for x = 128 or x = 200 is wider?
If anyone can help by please providing advice, I would be deeply appreciative.
The answers (below) in the prediction interval equations appear to be wrong; therefore, the upper and lower boundary limits were used from the model summary output table to denote the margins above and below the y value.