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 2012.

6. The actual number of colonies in 2012 was 2624. Complete the following sentence:

The residual for 2012 is  . This means the number of colonies in 2012 is
A. the same as
B. higher than
C. lower than
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. Yes, because 1982 is a reasonable year to predict data for.
C. No, because 2702.7841 number of colonies is too large to be a reasonable number of colonies, even for this year.

Answer 1

1.The relationship between year and number of honeybee colonies is negative weak and linear.

2. The explanatory variable is year and the response variable is colonies .

3. The equation for the regression line is

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

In 2 years, the number of colonies are expected to decrease by 7.542

Explanation:

Let us consider the regression equation
y = a + bx
In this equation
y is the dependent variable.(the one we are trying to predict)
x is the independent variable( or the predictor variable)
a is the y-intercept (The point on the y axis, where the regression line cuts it in the graph)
b is the coefficient or the slope of the variable.
We can have many variable and each variable will have a coefficient.

Interpreting the meaning of the coefficient
check two thing from the regression output
= the sign of the coefficient
- the value of the coefficient.

The sign (positive or negative) indicates whether the predictor variable increase or decrease the dependent variable.
The value indicates the value or magnitude of the change.
We state it as follows: one unit increase in x (independent variable) causes an increase/decrease (depends on the sign) of (value of the coefficient of the variable) in y (dependent variable)
For example : one unit increase in x , cause an increase of b units in y.

5. Use the regression equation to estimate the number of colonies in 2012.

6. The actual number of colonies in 2012 was 2624. Complete the following sentence:

residual = actual - predicted = 2624 - 2476.5104 = 147.4896

The residual for 2012 is 147.4896 . This means the number of colonies in 2012 is
B. higher than
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.