Deterministic Linear Relationships A deterministic linear relationship is one in

Question

Deterministic Linear Relationships A deterministic linear relationship is one in which there is no uncertainty in the linear relationship between y and x (they are perfectly correlated). So plugging x into the relationship will yield the exact value of yi . we can describe such a relationship as is the y-intercept (the value of y when x = 0), is the slope coefficient (the amount y changes when x is one unit larger). Note that we do not need a residual term when the relationship is deterministic. Consider a data set of elementary school students surveyed at the end of 2017. The data set has the following variables. o namet - First name of studenti . birthyeart - The year individual i was born. · ageyears1-The age of individual i in years at the time of the survey. · agedecadesl-The age of individual i in decades at the time of the survey (fractions allowed) . yearsuntil21- Remaining birthdays until individual i is 21 years old (including 21st birthday). For example, if Leo is born in 2010 his data would look like this: name birthyear Lagevears agedecades yearsuntil21 Leo 2010 7 0.7 14 Specify the values of , , and the correlation coefficient (R) for the following linear relationships. Hint: f you're unsure where to start, try adding a few more students born in different years to create a hypothetical sample and plot out the relevant scatter plot for each linear equation. 2) agedecades, = + birthyearí 3) yearsunti 21,- + birthyear

Explanation / Answer

1) by using the data from the table and putting it in the equation ageyear= +birthyear and solving the linear equation we can find the value as =2017,=-1, R=-1

2) by using the data from the table and putting it in the equation ageyear= +birthyear and solving the linear equation we can find the value as =201.7, =-0.1, R=-1

3) by using the data from the table and putting it in the equation ageyear= +birthyear and solving the linear equation we can find the value as =-1996, =1, R=1

data name birthyear ageyears agedecades yearsuntil21 leo 2010 7 0.7 14 sam 2008 9 0.9 12 amar 2012 5 0.5 16 coolin 2016 1 0.1 20 adam 2004 13 1.3 8

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