Exam 13: Correlation and Linear Regression

A study is designed to evaluate the relationship between a person's height and his or her salary.A random sample of 800 workers at a large corporation is drawn, and each individual's height (x) and salary (y) are recorded.If the coefficient of determination from the sample is 0.126, we can conclude that:

Consider these five x, y pairs. ​ ​ The regression equation is What is ?

The multiple linear regression model assumes:

From a random sample of n = 6 college students, a school counselor obtained the students' high school GPAs (x) and their college GPAs (y).Using these data, she wishes to develop a model that will allow her to predict a student's college GPA from his or her high school GPA. ​ ​ What is the fitted least-squares regression equation?

The least-squares method for determining the best fit minimizes the:

The equation (where E is a random variable) represents:

In the late 1890s, scientists first noted that the frequency of a cricket's chirps is related to air temperature.For each of 30 crickets, the frequency of chirping (in chirps per minute) and the air temperature (in degrees Fahrenheit) were recorded, and a regression analysis was performed. ​ Given that Sxx= 14,497.9 and 117.067, what is a 95% confidence interval for the mean air temperature when a cricket is chirping at a frequency of 120 chirps per minute?

Which value of the correlation coefficient r indicates a stronger correlation than 0.72?

Consider the following regression summary: ​ What proportion of the Y3 variability is explained by the model?

Consider the following regression analysis for predicting sales per week from intelligence and extroversion scores: ​ What proportion of the variability in sales per week is explained by the model?

The appropriate pattern for a residual plot is:

Medical researchers conducted a study designed to evaluate the relationship between blood pressure (y), age (x1), and cholesterol (x2).They proposed a linear model.A total of 126 individuals were randomly sampled, and blood pressure, age, and cholesterol were recorded for each.The regression summary appears here: ​ Which predictor (if any) does not appear to be linearly correlated with blood pressure? Which reason supports your answer?

Consider the following regression analysis for predicting sales per week from intelligence and extroversion scores: ​ What is a 90% confidence interval for the average sales per week for all people with an intelligence score of 103 and an extroversion score of 19?

In simple linear regression, the test statistic t is:

Which of the following is NOT an assumption for the simple linear regression model?

Is it always possible to do a linear best fit to a data set?

Consider the following regression summary: ​ Perform a global utility test for the model.State the correct decision and reasoning.(Use α = 0.01.)

If the correlation coefficient r is 0.81, what percentage of variation in the dependent variable is explained by a linear regression with the independent variable?

According to the spurious correlations website (https://www.tylervigen.com/spurious-correlations), there is a 0.985065 correlation from 2000 to 2009 between revenue from arcade games and the number of computer science doctorates awarded in the United States.Assuming this correlation reflects a real cause-effect relationship, what is a possible link between these two factors?

What is the difference between a general additive probabilistic model and a general deterministic model?