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 Footwear5 (FW5). Barefoot represents a subject's range of ankle motion (in degrees) while barefoot, and Footwear5 (FW5) represents their range of ankle motion (in degrees) while wearing compression hosiery and medical 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 compression hosiery and medical shoes, ?̂ y^ , based on their range of ankle motion while barefoot, ?x . Round your coefficients to two decimal places of precision.

?̂ y^ =

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

?̂ =y^=

Suppose Jan's actual range of ankle motion while wearing compression hosiery and medical shoes is 9.79°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, ?=0.53r=0.53 .

Barefoot	FW1	FW2	FW3	FW4	FW5
34.851	32.927	37.455	31.719	27.937	27.483
17.309	18.468	11.617	23.863	26.681	20.687
30.921	32.616	31.59	37.228	27.908	32.626
23.067	28.614	23.782	23.766	25.293	21.336
26.665	26.056	24.749	24.809	30.978	28.229
24.865	28.931	31.218	22.463	25.386	21.749
23.64	37.264	27.016	27.615	29.044	30.889
27.416	30.716	22.181	27.281	31.016	37.565
18.079	20.052	17.486	11.296	20.909	14.573
19.659	21.54	20.186	20.369	17.609	22.501
32.875	30.725	28.188	28.678	29.013	29.013
12.859	16.772	16.289	12.07	14.428	24.308
23.155	24.625	18.363	24.325	31.178	22.121
21.66	31.301	25.894	25.893	27.762	25.498
21.808	24.97	19.964	23.087	25.475	20.586
27.784	20.623	21.233	30.305	27.119	26.509
26.953	33.153	27.35	23.463	33.045	24.015
21.203	25.033	20.387	33.77	28.263	23.86
26.065	34.133	22.761	26.053	29.894	23.954
16.658	27.805	15.032	26.853	27.778	20.402
30.123	28.414	27.457	26.625	27.539	23.434
15.447	22.073	15.2	33.395	22.7	20.321
23.924	25.478	19.357	20.732	29.334	20.325
13.807	24.112	21.877	20.653	26.294	26.093
16.114	16.365	12.127	17.134	23.874	17.643
22.533	29.161	30.178	25.869	31.884	19.14
23.005	18.487	19.135	21.793	20.111	19.14

Answer 1

The The least square regression equation is defined as,

Under the Homoskedasticity assumption, the expected value of error term u_i will be zero

Now, the regression analysis is done in excel by following steps

Step 1: Write the data values in excel. The screenshot is shown below,

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: 'FW5' column, Input X Range: 'Barefoot' column then OK. The screenshot is shown below,

The result is obtained,

The least square regression equation is,

Jan's range of ankle motion for barefoot = 7.26,

Residual

Jan's actual range of ankle motion while wearing compression hosiery and medical shoes is 9.79

Correlation

r = 0.53

(This question part is incomplete)