Chapter PII, Problem 5RE

(a)

To determine

To find the equation of the regression line for predicting the number of twin births.

Answer to Problem 5RE

   .

Explanation of Solution

The table for the number of twins born in the United States increasing numbers are given in the question. For calculating the regression line we will use the Excel. First we will select the data given in the question and then go to the insert tab and select the scatterplot. Then the scatterplot of the data will appear. Then, we will go to the quick layout option from above and select the quick layout option with the regression line on it. Then the regression line would be as,

  

  

(b)

To determine

To explain in this context what the slope means.

Explanation of Solution

The table for the number of twins born in the United States increasing numbers are given in the question. Then the regression line would be as,

  

Thus, from the regression line, we can interpret the slope of the line as that every year the amount of twin births should increase by approximately by $2618.3$ .

(c)

To determine

To predict the number of twin births in the united states for the year $2010$ and comment on your faith in that prediction.

Answer to Problem 5RE

There are $143102.90$ twin births in the year $2010$ .

Explanation of Solution

The table for the number of twins born in the United States increasing numbers are given in the question. Then the regression line would be as,

  

Thus, to predict the number of twin births in the united states for the year $2010$ , it is calculated as,

  

Thus, there are $143102.90$ twin births in the year $2010$ . This prediction is possible but not likely to be exact because there is a curve in the graph and the value is an extrapolation.

(d)

To determine

To comment on the residual plot.

Explanation of Solution

The table for the number of twins born in the United States increasing numbers are given in the question. Then the regression line would be as,

  

We will now use the Minitab to find the residual plot. From the Stat menu, choose Regression. From the Regressionsubmenu, select Regression again. In the Regression dialog, enterthe response variable name in the “Response” box and thepredictor variable name in the “Predictor” box. To specify savedresults, in the Regression dialog, click Storage. Check “Residuals”and “Fits.” Click OK. To specify displays, in the Regressiondialog, click Graphs. Under “Residual Plots,” select “Individualplots” and check “Residuals versus fits.” Click OK. Now back inthe Regression dialog, click OK. Minitab computes the regressionand the requested saved values and graphs.

  

Thus, from the residual plot, we can say that the residual show a definite curve so the scatterplot is not linear.