Question

9 of 10 (0 complete) tween a child's height, x, and head circumference, y. She randomly selects 11 children from her our 0 Data Table th pret he Height (inches), x 27.5 24.25 25.25 26.25 25 mere Head Circumference (inches), y 17.6 17.2 17.2 17.6 16.9 17.7 17.4 17.6 17.4 17.6 17.6 is pre 27.75 26.5 27.25 26.75 26.75 27.75 is pre Et choi Print Done

Answer 1

Solution:

We can use the excel regression data analysis tool to answer the given questions. The excel output is given below:

SUMMARY OUTPUT Regression Statistics Multiple R 0.8475 R Square 0.7182 Adjusted R Square 0.6869 Standard Error 0.1377 Observations 11 MS 0.4348 0.0190 F 22.9376 Significance F 0.0010 ANOVA df SS Regression 1 0.4348 Residual 9 0.1706 Total 0.6055 Intercept Coefficients Standard Error Intercept 12.728 0.984 Height (inches), 0.178 0.037 Slope Stat 12.935 4.789 P-value 0.000 0.001 Lower 95% 10.502 0.094 Upper 95% 14.954 0.262

and head circumferencey She randomly selects 11 children from her practice measures their heights and head circum A pediatrician wants to determine the relation that exists between a child's height and obtains the accompanying data. Complete parts (a) through (g) below Click the icon to view the children's data (a) Find the least squares regression lina treating height as the explanatory variable and head circumference as the response variable 9 = =0.178x +(12.728) (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, appropriate Interprete slope. Select the correct choice below and necessary, in the answer box to complete your choice. O A For Every inch increase in head circumference, the height increased by in, on average (Round to three decimal places as h ed) 0.178 B. For every inch increase in height, the head circumference increases by in, on average (Round in three decimal places as needed) OC. For a head circumference of inches the height is prestad to be in (Round to three decimal places neded.) OD. For a height of inches, the head circumference is predicted to be in (Round to three decimal places as needed) OE niso appropriate to interpret the slope e answer box to contevour choice the correct choice below and if necessari Interpret the interest appropriate

Interpret the y-intercept, Happropriate. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. For a head circumference of inches, the height is predicted to be in (Round to three decimal places as needed.) OB. For a height of inches, the head circumference is predicted to be in (Round to three decimal places as needed.) O C. For every inch increase in head circumference, the height increases by in, on average (Round to three decimal places as needed.) OD. For every inch increase in height, the head circumference increases by in., on average. (Round to three decimal places as needed) - E it is not appropriate to interpret the y-intercept le) Use the regression equation to predict the head circumference of a child who is 25 inches tall. 17.18 Y =0.178x25+(12.728)=17.18 (Round tono decimal places as needed)

(d) Compute the residual based on the observed head circumference of the 25-inchal child in the table. Is the head circumference of this child above or below the value predicted by the regression model? 16.9-17.18=-0.28 -0.28 less than The residual for this observation is meaning that the head circumference of this child is the value predicted by the regression model {Round to two decimal places as needed) To Draw the least squares regression line on the scatter diagram of the data and label the residual from partid choosinc a OA OB 18 Click to select your answer

(1) Notice that two children are 26.75 inches tall. One has a head circumference of 17.4 inches: the other has a head circumference of 17,6 inches. How can this be? A. For children with a height of 26.75 inches, head circumferences vary UB. The only explanation is that the difference is due to the fact that one observation was of a boy, and one observation was of a giri. O C. There is no logical explanation for this the two observations in question should have had the same head circumference OD. The only explanation is that the difference was caused by measurement error Ig) Would it be reasonable to use the last squares regression line to predict the head circunference of a child who was 32 inches tall? Why? O A Yes-this height is possible and within the scope of the model O B. Yes-the calculated model can be used for any child's heighi. OC. No this height is not possible. D. Nothis, height is outside the scope of the model. O E. More information regarding the child is necessary to make the decision Click to select your answers.)