chapter 1

Chapter 12: Simple Linear Regression and Correlation83. Using Minitab, we create a scatterplot to see if a linear regression model is appropriate.7blood glucose level6540 10 20 30 40 50 60timeA linear model is reasonable; although it appears that the variance in y gets larger as xincreases. The Minitab output follows:The regression equation isblood glucose level = 3.70 + 0.0379 timePredictor Coef StDev T PConstant 3.6965 0.2159 17.12 0.000time 0.037895 0.006137 6.17 0.000S = 0.5525 R-Sq = 63.4% R-Sq(adj) = 61.7%Analysis of VarianceSource DF SS MS F PRegression 1 11.638 11.638 38.12 0.000Residual Error 22 6.716 0.305Total 23 18.353The coefficient of determination of 63.4% indicates that only a moderate percentage of thevariation in y can be explained by the change in x. A test of model utility indicates that timeis a significant predictor of blood glucose level. (t = 6.17, p = 0.0). A point estimate for bloodglucose level when time = 30 minutes is 4.833%. We would expect the average bloodglucose level at 30 minutes to be between 4.599 and 5.067, with 95% confidence.84.a. Using the techniques from a previous chapter, we can do a t test for the difference of twomeans based on paired data. Minitab’s paired t test for equality of means gives t = 3.54,with a p value of .002, which suggests that the average bf% reading for the two methodsis not the same.391