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.

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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.