Section 1
Simple Linear Regression
Give the y-intercept and slope for the line.$$y=2 x+1$$
Give the y-intercept and slope for the line.$$y=-2 x+1$$
Give the y-intercept and slope for the line.$$y=2 x+3$$
Give the equation and graph for a line with y-intercept and slope given in Exercises.$$y \text { -intercept }=3 ; \text { slope }=-1$$
Give the equation and graph for a line with y-intercept and slope given in Exercises.$$y \text { -intercept }=-3 ; \text { slope }=1$$
Give the equation and graph for a line with y-intercept and slope given in Exercises.$$y \text { -intercept }=2.5 ; \text { slope }=0$$
Give the equation and graph for a line with y-intercept and slope given in Exercises.$$y \text { -intercept }=-2.5 ; \text { slope }=5$$
What is the difference between deterministic and probabilistic models?
What are the assumptions made about the random error $\epsilon$ in the probabilistic model $y=\alpha+\beta x+\epsilon ?$
Independent and Dependent Variables Identify which of the two variables in Exercises $10-14$ is the independent variable $x$ and which is the dependent variable $y .$ Number of hours spent studying and grade on a history test.
Independent and Dependent Variables Identify which of the two variables in Exercises $10-14$ is the independent variable $x$ and which is the dependent variable $y .$ Number of calories burned per day and the number of minutes running on a treadmill.
Independent and Dependent Variables Identify which of the two variables in Exercises $10-14$ is the independent variable $x$ and which is the dependent variable $y .$Speed of a wind turbine and the amount of electricity generated by the turbine.
Independent and Dependent Variables Identify which of the two variables in Exercises $10-14$ is the independent variable $x$ and which is the dependent variable $y . Number of ice cream cones sold by Baskin Robbins and the temperature on a given day.
Independent and Dependent Variables Identify which of the two variables in Exercises $10-14$ is the independent variable $x$ and which is the dependent variable $y . Weight of a newborn puppy and litter size.
Calculate the sums of squares and cross-products, $S_{x x}$ and $S_{x x}$$$(3,6) \quad(5,8) \quad(2,6) \quad(1,4) \quad(4,7) \quad(4,6)$$
Calculate the sums of squares and cross-products, $S_{x x}$ and $S_{x x}$$$\begin{array}{c|ccc}x & 1 & 3 & 2 \\\hline y & 6 & 2 & 4\end{array}$$
Find the least-squares line for the data. Plot the points and graph the line on the same graph. Does the line appear to provide a good fit to the data points?$$\begin{array}{c|rrrrr}x & -2 & -1 & 0 & 1 & 2 \\\hline y & 1 & 1 & 3 & 5 & 5\end{array}$$
Find the least-squares line for the data. Plot the points and graph the line on the same graph. Does the line appear to provide a good fit to the data points?$$\begin{array}{c|cccccc}x & 1 & 2 & 3 & 4 & 5 & 6 \\\hline y & 5.6 & 4.6 & 4.5 & 3.7 & 3.2 & 2.7\end{array}$$
Use the data entry method in your scientific calculator to enter the measurements. Recall the proper memories to find the y-intercept, $a,$ and the slope, $b$, of the line. $$\begin{array}{c|rrrrr}x & -2 & -1 & 0 & 1 & 2 \\\hline y & 1 & 1 & 3 & 5 & 5\end{array}$$
Use the data entry method in your scientific calculator to enter the measurements. Recall the proper memories to find the y-intercept, $a,$ and the slope, $b$, of the line. $$\begin{array}{c|cccccc}x & 1 & 2 & 3 & 4 & 5 & 6 \\\hline y & 5.6 & 4.6 & 4.5 & 3.7 & 3.2 & 2.7\end{array}$$
How good are you at estimating? To test a subject's ability to estimate sizes, he was shown 10 different objects and asked to estimate their length or diameter. The object was then measured, and the results were recorded in the table below.a. Find the least-squares regression line for predicting the actual measurement as a function of the esti-mated measurement.b. Plot the points and the fitted line. Does the assumption of a linear relationship appear to be reasonable?
Leonardo da Vinci $(1452-1519)$ drew a sketch of a man, indicating that a person's armspan (measuring across the back with your arms outstretched to make a "T") is roughly equal to the person's height. To test this claim, we measured eight people with the following results: a. Draw a scatterplot for armspan and height. Use the same scale on both the horizontal and vertical axes. Describe the relationship between the two variables.b. If da Vinci is correct, and a person's armspan is roughly the same as the person's height, what should the slope of the regression line be?c. Calculate the regression line for predicting height based on a person's armspan. Does the value of the slope $b$ confirm your conclusions in part b?d. If a person has an armspan of 157 centimeters, what would you predict the person's height to be?