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In Chapter 3, we examined data on the body weights and backpack weights of a group of eight randomly selected ninth-grade students at the Webb Schools. Some Minitab output from least-squares regression analysis for these data is shown

1. What conditions must be met for regression inference to be appropriate?

Short Answer

Expert verified

There are five conditions that must be met for the regression inferences to be appropriate.

Step by step solution

01

Given Information

Need to find the conditions that must be met for regression inference to be appropriate.

02

Explanation

There are five conditions that must be met for the regression inferences to be appropriate, that are:

Linear, independent, normal, equal variance, and random conditions.

Thus, we have to check the linearity of the relationship between variables, and then we have to check whether the variables are independent samples or not. Then, we have to check the normality of the residual whether they follow the normal distribution, and also check if they have equal variance. Also the sample we must have taken must be a random sample so that it represents the whole of the population.

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Most popular questions from this chapter

Marcella takes a shower every morning when she gets up. Her time in the shower varies according to a Normal distribution with mean 4.5minutes and standard deviation 0.9minutes.

(a) If Marcella took a 7-minute shower, would it be classified as an outlier? Justify your answer.

(b) Suppose we choose 10days at random and record the length of Marcellaโ€™s shower each day. Whatโ€™s the probability that her shower time is 7minutes or higher on at least 2of the days? Show your work.

(c) Find the probability that the mean length of her shower times on these 10 days exceeds5 minutes. Show your work

The swinging pendulum Refer to Exercise 33. Here is Minitab output from separate regression analyses of the two sets of transformed pendulum data:

Do each of the following for both transformations.

(a) Give the equation of the least-squares regression line. Define any variables you use.

(b) Use the model from part (a) to predict the period of a pendulum with length of 80 centimeters. Show your work.

(c) Interpret the value of s in context

The swinging pendulum Mrs. Hanrahanโ€™s precalculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-and-forth swing (called its period). Here are their data:

(a) Make a reasonably accurate scatterplot of the data by hand, using length as the explanatory variable. Describe what you see. (b) The theoretical relationship between a pendulumโ€™s length and its period is

period=2ฯ€glength

where gis a constant representing the acceleration due to gravity (in this case, g=980cm/s2). Use the graph below to identify the transformation that was used to linearize the curved pattern in part (a).

(c) Use the following graph to identify the transformation that was used to linearize the curved pattern in part (a).

Which of the following is a categorical variable?

(a) The weight of automobiles

(b) The time required to complete the Olympic marathon

(c) The average gas mileage of a hybrid car

(d) The brand of shampoo purchased by shoppers in a

grocery store

(e) The average closing price of a particular stock on the

New York Stock Exchange

An old saying in golf is โ€œYou drive for show and you putt for dough.โ€ The point is that good putting is more important than long driving for shooting low scores and hence winning money. To see if this is the case, data from a random sample of 69of the nearly 1000players on the PGA Tourโ€™s world money list are examined. The average number of putts per hole and the playerโ€™s total winnings for the previous season is recorded. A least-squares regression line was fitted to the data. The following results were obtained from statistical software.

Suppose that the researchers test the hypotheses H0:ฮฒ=0: Ha:ฮฒ<0. The value of the t statistic for this test is

(a)2.61

(b)2.44

(c)0.081

(d)-2.44

(e) -20.24

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