The honeybee dataset contains data collected from the USDA on the estimated number of honeybee colonies (in thousands) for the years 1995 through 2012. We use technology to find that a regression line to predict number of thousand) colonies from year (in calendar year) is:
Colonies = 19, 291,511-8.358(Year)
a. Interpret the slope of the line in context as done in the textbook.
b. Often researchers will adjust a year explanatory variable such that it represents years since the first-year data were collected. Why might they do this? (Hint: Consider interpreting the y-intercept in this regression line.)
c. Beginning with the equation and showing the steps, predict the bee population in 2100. State why or why not this prediction is appropriate.

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Respuesta :

AbsorbingMan AbsorbingMan · Answer 1 · 2021-02-12T06:25:05+01:00

Solution :

a). [tex]$\widehat{y} = 19291511 - 8.358 $[/tex] (year)

As one year increases, the honey bees decreases by 8.358 in thousands.

b). As the year is kept constant, at the start of the regression, the basic value of bees is 19291511 in 1995.

c). Prediction of population of homey bees in the year 2100.

x = 105

[tex]$\widehat{y} = 19291511-8.358(105)(1000)$[/tex]

= 19291511 - 877590

= 18413921

It is not an appropriate prediction as the year 2100 is out of the range of the given regression model.