12. Regression

In regression analysis, which method is commonly used to estimate the parameters of a linear model by minimizing the sum of the squared differences between observed and predicted values?$min\left(\sum _{i=1}^n{(y_i-{ŷ}_i)}^2\right)$

Which of the following is not one of the purposes of a line of regression in linear regression using the least squares method ($\text{least squares}$)?

In linear regression using the least squares method, which expression can be simplified to find the slope of the trend line in the scatterplot?

In linear regression using the least squares method, which of the following equations best approximates the line of best fit for a set of data points $(x,y)$?

Given the least squares regression equation $y=a+bx$, what does the coefficient $b$ represent?

In linear regression using the least squares method, the line of best fit for a scatterplot always passes through which pair of points?

In linear regression using the least squares method, which formula correctly represents the slope of the line of best fit for a set of data points $(x,y)$?

You Explain It! Study Time and Exam Scores

After the first exam in a statistics course, Professor Katula surveyed 14 randomly selected students to determine the relation between the amount of time they spent studying for the exam and exam score. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is:

ŷ = 6.3333x + 53.0298

c. What is the mean score of students who did not study?

"In Exercises 9 and 10, identify the explanatory variable and the response variable.

9. A nutritionist wants to determine whether the amounts of water consumed each day by persons of the same weight and on the same diet can be used to predict individual weight

loss."

Using the sample data from Problem 7 in Section 12.3

a. Predict the mean value of y if x=1.4.

4. For a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y.

In linear regression using the least squares method, what is the expected shape or equation of the calibration plot relating the dependent variable to the independent variable?

[DATA] Hurricanes [See Problem 14 in Section 12.3] The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.

c. Use the “Randomization test for slope” applet in StatCrunch to build the null model to generate at least 2000 repetitions of this study to obtain a P-value. Interpret the P-value.