According to the data reported by the New York State Department of Health regarding West Nile Virus for the years 2000-2004, the least squares line equation for the number of reported dead birds (x) versus the number of human West Nile virus cases (y) is ŷ = −10.2638 + 0.0491x. If the number of dead birds reported in a year is 520, how many human cases of West Nile virus can be expected? (Round your answer to the nearest whole number.) cases

The least square regression line is used to determine the relationship between a response variable (or dependent variable) and an explanatory variable (or independent variable).

The least square regression line can be used to predict the future value or estimate the past value of the dependent variable based on the independent variable.

The general form of a least square regression line is:

[tex]y=\alpha +\beta x[/tex]

Here,

y = response variable

x = explanatory variable

α = intercept

β = slope

The least square regression line for the number of reported dead birds (x) versus the number of human West Nile virus cases (y) is given by:

[tex]\hat y=-10.2638+0.0491 x[/tex]

Compute the predicted value of y for x = 520 as follows:

[tex]\hat y=-10.2638+0.0491 x[/tex]

[tex]=-10.2638+0.0491 \times 520\\=-10.2638+25.532\\=15.2682\\\approx 15[/tex]

Thus, the number of human cases of West Nile virus that can be expected, if the number of dead birds reported in a year is 520, is 15.