Data is available on the characteristics listed below for various cereals. Each of these cereals has been given a rating between 0 and 100. The output from a regression model to predict the Rating based upon the other characteristics of the cereal is provided. Calories: The number of calories in a serving. Protein: The amount of protein is a serving. Fat: The amount of fat in a serving. Fiber: The amount of fiber in a serving Sugars: The amount of sugar in a serving Potass: The amount of Potassium in a serving Vitamins: The percent of required daily vitamins in a serving.

The model that was estimated can be written as:

Y is the rating and the X's correspond to the input variables. For this data test the null hypothesis that . In other words, test the hypothesis that the coefficients for all the X's are equal to zero.

Regression Equation Rating = 59.64 - 0.1110 Calories + 2.741 Protein - 3.186 Fat + 2.650 Fiber - 1.485 Sugars - 0.0175 Potass - 0.0888 Vitamins Coefficients Term Coef SE Coef T-Value P-Value Constant 59.64 3.48 17.14 0.000 Calories -0.1110 0.0405 -2.75 01008 Protein 2.741 0.654 4.19 0.000 Fat -3.186 0.616 -5.17 0.000 Fiber 2.650 0.610 434 0.000 Sugars -1.485 0.160 -9.28 0.000 Potass -0.0175 0.0213 -0.82 0.415 Vitamins -0.0888 0.0236 -3.76 0.000 Model Summary S R-so R-so (adj) R-so[pred) 4.22503 91.81% 90.9495 89.2596 Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Regression 7 10528 1504.01 83.01 0.000 Error 65 1178 18.12 Total 72 11706Y= Bot SIXnitwit B Xnitei