Question

From 1995 to 2012, researchers surveyed the number of honeybee colonies in order to determine whether the population changed over time. The scatterplot below shows the relationship between these two variables along with the least squares fit. Round all calculated results to 4 decimal places.

1.The relationship between year and number of honeybee colonies is  ? positive negative ,  ? weak strong , and  ? linear non-linear .

2. The explanatory variable is  ? year days number of bees number of bee colonies  and the response variable is  ? year days number of bees number of bee colonies .

The summary statistics for number of colonies and year are listed below. The correlation between number of colonies and year is -0.3520 .

Year: mean = 2004.0625, standard deviation = 5.2086

Colonies: mean = 2536.3750, standard deviation = 111.5944

3. The equation for the regression line is y =  +  x

4.Complete the following sentence to interpret the slope of the regression line:

In 2 years, the number of colonies are expected to  ? decrease increase  by

5. Use the regression equation to estimate the number of colonies in 2004.

6. The actual number of colonies in 2004 was 2556. Complete the following sentence:

The residual for 2004 is  . This means the number of colonies in 2004 is
A. lower than
B. higher than
C. the same as
the number of colonies predicted by the regression model.

7. Would it be appropriate to use this linear model to predict the number of honeybee colonies in 1982?

A. No, because 1982 is beyond the range of the data used to build the regression model.
B. No, because 2702.7841 number of colonies is too large to be a reasonable number of colonies, even for this year.
C. Yes, because 1982 is a reasonable year to predict data for.

Answer 1