Question

Assume that the regression line for the New York City murder rate per 100,000 residents between 2000 and 2010 is given by y=−0.24x+488.7, where x is the year and y is the murder rate. Interpolate to get an approximate value for the rate in 2006. Round your answer to one decimal place.

Interpolated rate

The table below shows the murder rate per 100,000 residents for a large American city over a twelve-year period.

Year	2000	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011
Rate	8.8	7.1	7.2	6.8	6.4	7.1	5.8	6.1	5.4	6.2	6.1	4.9

Enter the coefficients of the regression line for this data, rounding each to two decimal places:
	Slope:		Intercept:
Use your regression line (with rounded coefficients) to estimate this city’s murder rate in 2012. Round your answer to the nearest tenth.
	Estimate:

The table below shows per capita cheese consumption, in pounds, for several years for one American state.

Year	2000	2001	2002	2003	2004	2006	2007	2008	2009
Cheese Consumed	26.1	26.8	28.2	28.8	29.8	29.6	31	30.8	32.1

Which of the following is the equation of the regression line for this data?

A. y=−0.595x+1163.4
B. y=1163.4x−0.595
C. y=0.595x−1163.4
D. y=0.595x+1163.4
E. y=1163.4x+0.595
F. y=−0.595x−1163.4

Using the regression line, estimate the per-capita consumption in 2005 to the nearest tenth of a pound.
	Estimate:
Did you just perform interpolation or extrapolation? A. interpolation B. extrapolation

Would you expect the regression line for the price of a camera vs. the number sold to slope up or down, or would it be pretty much horizontal?

A. up
B. down
C. horizontal

Answer 1

a) slope= -0.24  
intercept = 488.7  
==========

2)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	18040.00	263.20	82.22	31.24	48.92
mean	2004.44	29.24	SSxx	SSyy	SSxy

sample size ,   n =   9          
here, x̅ = Σx / n=   2004.444   ,     ȳ = Σy/n =   29.244  
               0.0145898  
SSxx =    Σ(x-x̅)² =    82.2222          
SSxy=   Σ(x-x̅)(y-ȳ) =   48.9          
                  
estimated slope , ß1 = SSxy/SSxx =   48.9   /   82.222   =   0.59500
                  
intercept,   ß0 = y̅-ß1* x̄ =   -1163.40000          
                  
so, regression line is   Ŷ =   -1163.4000   +   0.5950   *x

C. y=0.595x−1163.4

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Predicted Y at X=   2005   is          
Ŷ =   -1163.4000   +   0.5950   *2005=   29.6

interpolation

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As the price increases, we would expect the number sold to be decrease. Hence,
It will be a down slope.

answer: DOWN

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