You have a hot grill and an empty hamburger bun, but you have sworn off greasy hamburgers. Would a meatless hamburger do? The data for 12 brands of meatless hamburger were collected. Calories, fat, and sodium in these meatless hamburgers were used to predict taste score (between 0 and 100). The correlation between fat and calories is r = 0.828. How might this model be improved?
Predictor Coef SE Coef t-value P-value
Constant 69.42 23.84 2.91 0.020
calories -0.5772 0.2727 -2.12 0.087
fat 8.359 3.263 2.56 0.034
sodium 0.05116 0.03792 1.35 0.214
Answer
a. Omit predictors that are not useful one-by-one, until we’re left with only useful predictors.
b. Omit fat from the model.
c. Omit sodium and calories from the model.
d. Add new predictor variables to the model.
To determine how the model can be improved, we can analyze the predictor coefficients, standard errors, t-values, and p-values.
Looking at the provided data, the predictor coefficients suggest that calories, fat, and sodium have an influence on the taste score of meatless hamburgers. However, we need to consider the significance of each predictor.
One way to improve the model is to look at the p-values. The p-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Lower p-values indicate stronger evidence against the null hypothesis.
In the given data, the p-values for calories, fat, and sodium are 0.087, 0.034, and 0.214, respectively. Based on these p-values, calories and fat appear to be more significant predictors compared to sodium.
Therefore, one approach to improve the model would be to eliminate the predictor with the highest p-value, which is sodium in this case. By removing sodium from the model, we can simplify it and potentially increase its overall accuracy.
Hence, the correct choice to improve the model would be option c: omit sodium and calories from the model.