Exam 10: Correlation and Regression

An environmentalist wants to determine the relationship between the number (in thousands) of forest fires over the year and the number (in hundreds of thousands) burned. The data for 8 recent years are shown. a. Draw the scatter plot for the variables. b. Give a brief explanation of the type of relationship. Number of fires x Number of acres burned 72 62 69 42 58 19 47 26 84 51 62 15 57 30 45 15

Find the equation of the regression line. x 50 58 43 52 47 42 y 184 187 163 171 171 144

In a study of reaction times, the time to respond to a visual stimulus $( x )$ and the time to respond to an auditory stimulus $( y )$ were recorded for each of 6 subjects. Times were measured in thousandths of a second. The results are presented in the following table. The following MINITAB output describes the fit of a linear model to these data. Assume assumptions of the linear model are satisfied. The regression equation is Auditory $= 193.269291 + 0.354955$ Visual Predictor Coef SE Coef Constant 193.269291 16.307408 11.851625 0.000291 Visual 0.354955 0.086702 4.093976 0.014927 What is the slope of the least-squares regression line?

If the equation for the regression line is $y ^ { \prime } = 9 x + 2$ , then a value of $x = - 3$ will result in a predicted value for $y$ of

Two researchers run identical experiments except researcher A collects twice as many points as researcher B. For a specific value $x$ , researcher A estimates a $y$ value of $y _ { A } ^ { \prime }$ and researcher B estimates a $y$ value of $y _ { B ^ { \prime } }$ . We would expect that researcher $\mathrm { A } ^ { \prime } \mathrm { s } 95 \%$ prediction interval around $y _ { A } ^ { \prime }$ to be, in general,

If the correlation coefficient $r$ is equal to $0.547$ , find the coefficient of determination and the coefficient of nondetermination.

The variation due to chance, found by the formula , is called the unexplained variation.

In a multiple regression model $y ^ { \prime } = - 9 + 3 x _ { 1 } + 21 x _ { 2 } + 13 x _ { 3 } + 4 x _ { 4 }$ , if the $x _ { 1 }$ value changes by 2 , then the predicted value for $y$ will change by

Compute the value of the correlation coefficient. x 40 43 46 41 44 y 182 214 210 194 218

With enough variables, it is possible to get an $R ^ { 2 }$ value close to 1 , even if the variables have no particular meaning in the model

When $r$ is not significantly different from 0 , the best predictor of $y$ is the___________ of the data values of $y$ .

A psychologist wants to determine if there is a linear relationship between the nun hours a person goes without sleep and the number of mistakes he/she makes on a : test. The following data is recorded. a. Draw a scatter plot. b. Determine the regression line equation and plot the regression line on the scatter plot. Hours without Sleep, Number of Mistakes, y 32 6 38 8 48 13 24 5 46 7 35 6 30 5 34 8 42 12

A regression line can be used to show trends in data.

Compute the standard error of the estimate for the data below. X values 54 63 70 84 97 Y values 94 122 146 167 191

An experiment is carried out to determine the relationship between the average speed (rpm) and power (hp) of a mixer. Draw the scatter plot for the variables. Average Speed Power 325.0 1.10 348.9 1.40 312.9 1.07 230.0 0.25 269.2 0.64 305.0 0.93

As a researcher collects more and more data, the 95% prediction intervals in general