Exam 13: Correlation and Linear Regression

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 067, what is a 90% prediction interval for the air temperature when a cricket is chirping at a frequency of 120 chirps per minute?

In simple linear regression, most often we perform a two-tailed test of the population slope to determine whether there is sufficient evidence to infer that a linear relationship exists.The null hypothesis is stated as:

An instructor's records show a 0.956 correlation between grades and attendance.If the correlation implies causality, what might this imply?

In a simple linear regression, if the coefficient of determination is 0.94, then:

The linear regression model assumes the error random variable is:

In the linear regression model, the homogeneity of variance assumption basically means:

In the following residual plot:

The confidence interval estimate of the expected value of y for a given value of x, when compared to the prediction interval of y for the same given value of x at the same confidence level, will be:

According to the spurious correlations website (https://www.tylervigen.com/spurious-correlations), there is a 0.952407 correlation from 1999 to 2010 between people who drowned after falling from a fishing boat and the marriage rate in Kentucky.This shows that:

If the sample correlation coefficient is -0.95, what can we conclude?

We record the amount of time (x in minutes) per day that a group of 12 high school students spend using their cell phone (texting, talking, and web use).We also record the overall GPA (y) of each student.Following a regression summary for these data: ​ ​ Does there appear to be a significant linear relationship between the amount of cell phone use and GPA? (Use α = 0.01.)

Given a specific value of x and a confidence level, which of the following statements is correct?

We record the amount of time (x in minutes) per day that a group of 12 high school students spend using their cell phone (texting, talking, and web use).We also record the overall GPA (y) of each student.Following is a regression summary for these data: ​ ​ What is a 95% confidence interval for the average GPA change associated with a 1-min increase in average daily cell use (β1)?

The statement that "correlation does not imply causality" indicates that:

In simple linear regression, the plot of residuals versus fitted values should:

From the following residual versus fit plot, it appears that:

In a regression analysis, the residuals represent:

The following ANOVA table describes a simple linear regression on two arbitrary variables x and y. ​ ​ Based on the output, does there appear to be a significant linear relationship between x and y? Select the appropriate critical value (CV), test statistic (TS), and decision.(Use α = 0.01.)

Ten used cars from a rental fleet are randomly selected.Each vehicle's annual maintenance cost from the previous calendar year (y) is recorded as well as the vehicle's current mileage (x).A simple linear regression is conducted on the data. ​ What is an 80% prediction interval for the annual repair cost of a used vehicle with 40,000 miles? (Given: Sxx= 8,036,677,024 and = $43,627.700.)

If the sum of squares for error (SSE) is equal to zero, then the coefficient of determination, r2, must be: