Question

Problem Value: 1 point(s). Problem Score: 62%. Attempts Remaining: Unlimited. (1 point) 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. 2700 2600 Colonies 2500 2400 2300 1995 2000 2010 2005 Year 1. The relationship between year and number of honeybee colonies is negative. weak and linear A. 2. The explanatory variable is year and the response variable is 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 -0.3779 Year: mean = 2002.6875, standard deviation = 5.0822 Colonies: mean = 2552.5000, standard deviation = 114.1607 3. The equation for the regression line is y = 21293.62 + -7.6259 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 by 15.2518 5. Use the regression equation to estimate the number of colonies in 1997. 6. The actual number of colonies in 1997 was 2631. Complete the following sentence: . This means the number of colonies in 1997 is The residual for 1997 is A. higher than the same as

Answer 1

3)

	x̅ =		2002.6875
	y̅ =		2552.5
	sx=		5.0822
	sy =		114.1607
	r=		-0.3779
slope b1=r*sy/sx=			-8.4887
intercept bo=y̅ +r(sy/sx)*(x̅)=			19552.7360

y^ =19552.7360+(-8.4887)*x

4)

decreases by 8.4887

5)

predicted value =-8.4887*1997+19552.7360=

2600.7795

6) residual=actual-predicted value = 2631-2600.7795 =30.2205