Question

Range of ankle motion is a contributing factor to falls among the elderly. Suppose a team of researchers is studying how compression hosiery, typical shoes, and medical shoes affect range of ankle motion.

In particular, note the variables Barefoot and Footwear1. Barefoot represents a subject's range of ankle motion (in degrees) while barefoot, and Footwear1 represents their range of ankle motion (in degrees) while wearing typical shoes.

Use this data and your preferred software to calculate the equation of the least-squares linear regression line to predict a subject's range of ankle motion while wearing typical shoes, y^ , based on their range of ankle motion while barefoot, x . Round your coefficients to two decimal places of precision.

?̂ =

A physical therapist determines that her patient Jan has a range of ankle motion of 7.26° while barefoot. Predict Jan's range of ankle motion while wearing typical shoes, ?̂ . Round your answer to two decimal places.

?̂ =

°

Suppose Jan's actual range of ankle motion while wearing typical shoes is 9.79° . Use her predicted range of ankle motion to calculate the residual associated with this value. Round your answer to two decimal places.

residual=

°

In order to assess the linear regression equation's ability to predict range of ankle motion, the physical therapist reviewed a scatterplot of the researchers' sample data and calculated the correlation, r=0.64 .

Step 1

**Introduction:**

Here, the response variable, *y*, is the range of ankle motion while wearing typical shoes. The values of this variable are given in the column “FW1”.

The predictor variable, *x* is the range of ankle motion while barefoot. The values of this variable are given in the column “Barefoot”.

Step 2

**Calculation:**

The regression analysis can be performed using Excel.

Consider the data entered as in the image you have provided. Rename the first column, that is, the column named Barefoot as *x*, and the second column, that is, the column named FW1 as *y*, for convenience.

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