Stats HWRK Ch.4 Regression
Match the linear correlation coefficient to the scatter diagram. The scales on the x- and y-axis are the same for each scatter diagram. (a) r=0.946, (b) r=1, (c)= 0.787
(a) Scatter diagram II. (b) Scatter diagram III. (c) Scatter diagram I.
If r=_______, then a perfect negative linear relation exists between the two quantitative variables.
-1
Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following. A. Do the two variables have a linear relationship? B. If the relationship is linear do the variables have a positive or negative association?
A. The data points do not have a linear relationship because they do not lie mainly in a straight line. B. The relationship is not linear.
Determine whether the scatter diagram indicates that a linear relation may exist between the two variables. If the relation is linear, determine whether it indicates a positive or negative association between the variables. Use this information to answer the following. A.Do the two variables have a linear relationship? B. Do the two variables have a positive or a negative association?
A. The data points have a linear relationship because they lie mainly in a straight line. B.The two variables have a negative association.
A data set is given below. (a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y. (b) Given that x=3.6667, sx=2.3381, y=4.1333, sy=1.7907, and r=−0.9474, determine the least-squares regression line. (c) Graph the least-squares regression line on the scatter diagram drawn in part (a). x: 1 1 3 5 6 6 y: 5.2 6.5 5.4 3.0 2.2 (a) Choose the correct graph below. There appears to be ____relationship (b) y=__x=__ (c) Choose the correct graph below.
A. a. a linear, negative B. (y-hat) y= -0.726x +6.794 C.
A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the accompanying data. Complete parts (a) through (g) below. (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. First interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Interpret the y-intercept, if appropriate. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. (d) Compute the residual based on the observed head circumference of the 25-inch-tall child in the table. Is the head circumference of this child above or below the value predicted by the regression model? (e) Draw the least-squares regression line on the scatter diagram of the data and label the residual from part (d). Choose the correct graph below. (f) Notice that two children are 26.5 inches tall. One has a head circumference of 17.5 inches; the other has a head circumference of 17.7 inches. How can this be? (g) Would it be reasonable to use the least-squares regression line to predict the head circumference of a child who was 32 inches tall? Why?
A.y=0.158x+13.4 B.For every inch increase in height, the head circumference increases by 0.158 in., on average. It is not appropriate to interpret the y-intercept. C. y= 17.34 in D.The residual for this observation is −0.14, meaning that the head circumference of this child is below the value predicted by the regression model. E. c F. For children with a height of 26.5 inches, head circumferences vary. G.No—this height is outside the scope of the model.
Is the statement below true or false? The least-squares regression line always travels through the point x,y(with the lines on top).
True The statement is true. The least-squares regression line is y=b1x+b0 where b0=y−b1x. That means that by definition, the predicted value for x is b1x+y−b1x which simplifies back to y.
The given data represent the total compensation for 10 randomly selected CEOs and their company's stock performance in 2009. Analysis of this data reveals a correlation coefficient of r=−0.2130. What would be the predicted stock return for a company whose CEO made $15 million? What would be the predicted stock return for a company whose CEO made $25 million? What would be the predicted stock return for a company whose CEO made $15 million?
What would be the predicted stock return for a company whose CEO made $15 million? 17.3% What would be the predicted stock return for a company whose CEO made $25 million? 17.3%
Match the coefficient of determination to the scatter diagram. The scales on the x-axis and y-axis are the same for each scatter diagram. (a) R2=0.27, (b) R2=0.90, (c) R2=1
(a) Scatter diagram III. (b) Scatter diagram I. (c) Scatter diagram II.
