Question

History Window Help MATHEMATICAL ASSOCIATION OF AMERICA Looged in an webwork /mustat 1200 wbwk6 10 WBWK6: Problem 10 Prev Up Next Answer Preview Result Messages Variable 'n' is not defined in this context The answer above is NOT correct 2 pts) Because elderly peopie may have difficulity standing to have their height measured, a study looked at the relationship between overall height and height to the knee. Here are data (in centimetars) for five elderly men KneeHeight X 56 44 41 44 551 Heighty 190150 145 165 160 What is the equation of the least-squares regression line for predicting heignt from knee height? (Compute values to three decimal places of accuracy-) ANSWER: y. 78.204+1.739x Preview AnswersSubmit Answers Your score was recorded You have attempted this probiem 1 time. You rooeved a score of 096 for this attempt Your overal recorded score is 096. Ps

Answer 1

To find the regression coefficients for the equation: $y = \beta _{0}+\beta _{1}x+\epsilon$ Let b₀ and b₁ denote the estimates of the intercept $\beta _{0}$ and slope parameter $\beta _{1}$

Using the formula for the intercept and slope,

$b _{1}=\frac{\sum xy-n\overline{x}\overline{y}}{\sum x^{2}-n\overline{x}^{2}} ,b _{0}=\overline{y}-b_{1}\overline{x}$

Computing the values, $\overline{x}= \frac{190+150+..+169}{5}=163.8$ and $\overline{y}= \frac{56+44+...+55}{5}=48$

Substituting the values, $b _{1}=\frac{\sum xy-n\overline{x}\overline{y}}{\sum x^{2}-n\overline{x}^{2}}=\frac{39740-5(163.8)(48)}{135411-5(163.8)^{2}}=0.340$      

$b _{0}=\overline{y}-b_{1}\overline{x}=48-0.340(163.8)=-7.693$

Hence, the predicted equation of least square regression line is given by,

${\color{Red}y = -7.693 + 0.340x }$