Finding the better model In a statistics class last spring the students measured

Question

Finding the better model In a statistics class last spring the students measured their height, their arm span (finger tip to finger tip), and the length of their forearm (elbow to finger tip) All distances were measured in inches eight, their arm span or We collected data to answer this question which is a better predictor of someone's h their torearm length height? ? In other words, will someone's forearm length or their arm span more accurately predict their Listed below are the data that were collected Forearm ength Student Arm Height span 60.5 17.5 16.6 17 17 16.5 18 18.5 67 61 65 62.5 62.5 68 71.5 B. 64.5 63.5 61.5 67 67 To do: Use your skills trom Chapter 6 -8 to create the better linear regression ine to predict a pe do two inear regressions then determine which equation is "better than the other (Making a called "bu points, ilding a model because our whole goal is to find a line that is a realy good estimate of the patter of data Just like modeling clay is shaped to look like an object, the regression model is shaped to the pattern of the data.) Turn in: once youve determine the better linear regression, explain the following . which variable did you use to predict height arm span or forearm length? . Give the equation of the inear regression that best fits the data. Show your equation here. (Don't show you work here, use technology and then give the equation ) Use proper notation for the y both models: Compute and show us the correlation between the two variables Interpret the correlation in a sentence or two how strong is the relationship? is the relationship linear? is the relationship positive or negative? . For both models: Compute and show us the e and show us the coefficient of determination, and interpret it in a sentence what percent of the vaniation in y is explained by the rn

Explanation / Answer

Perform two regression analysis. Enter data in Minitab-Stat-Regression-Fitted Line Plot-type C3 in Response and C1 in Predictor to compute first regression line and then keep the reposne predictor as it is and chnage the Predictor to C2 to obtain the second regression line. The two regression lines are as follows:

Height=-0.45+1.022 Arm span (R^2=77.7%)

Height=-5.89+4.133 Forearm length (R^2=87.7%)

Based on the value of R^2, which is a measure of how close the data are to the fitted regression line, fore arm length is a better predictor.

The required regression line is: yhat=-5.89+4.133 x

Model1: Correlation coefficient, r1=sqrt R^2= sqrt (0.777)=0.88

Model2: Correlation coeffciient, r2=sqrt R^2=sqrt (0.877)=0.94

Coeffciient of determination for model 1: R1^2=0.777 (obtained from technology output)

Around 77.7% variation in height is explained by arm span.

Coeffciient of determination for model2: R2^2=0.877 (obtained from technology output)

Around 87.7% variation in height is explained by the forearm length.

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