(d) Develop an estimated regression equation for the data of the form ŷ = bo + b,x + b,x2. (Round b, to one decimal place and b, to two decimal places and b, to four decimal places.) (e) Use the results from part (d) to test for a significant relationship between x, x2, and y. Use a = 0.05. Is the relationship between x, x2, and y significant? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = Is the relationship between x, x², and y significant? O Yes, the relationship is significant. O No, the relationship is not significant. (f) Use the model from part (d) to predict the value of y when x = 25. (Round your answer to three decimal places.)

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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.