Question

For complete credit show all of your calculations, list your assumptions and formulas, draw relevant tables and plots all on handwritten pages in your notebook.

If there are repetitious calculations you only need to show an illustrative calculation.

price	lotsize
490000	2503
512000	2483
345000	2500
508670	2900
550000	2513
300000	2513
995000	4950
920000	3135
470000	2375
450000	2375

5.Calculate the weighted average of price and lotsize. Why are these the same or different from the median and arithmetic mean?

6.What is the correlation between price and lotsize?

7.For the model Y = a + bX + e, where Y = price, X = lotsize, e = deviation of Y from the conditional mean a + bX, what are the best estimators of the slope and the Y-intercept? Sketch the line with these parameters that runs through the scatterplot of Y and X. Be sure to draw the error bars from the data points to the line.

Answer 1

5)

here,

mean of lot size

x̅ = Σx / n=   2824.70

Median=0.5(n+1)th value =    5.5th   value of sorted data
=   2508.000  

mean of price

ȳ = Σy/n =   554067.00

Median=0.5(n+1)th value =    5.5th   value of sorted data
=   499335.000  

6)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	28247	5540670	5543310.1	462436764010.0	1315178451.00
mean	2824.70	554067.00	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.8214

......

7)

sample size ,   n =   10          
here, x̅ = Σx / n=   2824.70   ,     ȳ = Σy/n =   554067.00  
                  
SSxx =    Σ(x-x̅)² =    5543310.1000          
SSxy=   Σ(x-x̅)(y-ȳ) =   1315178451.0          
                  
estimated slope , ß1 = SSxy/SSxx =   1315178451.0   /   5543310.100   =   237.2551
                  
intercept,   ß0 = y̅-ß1* x̄ =   -116107.4091          
so, regression line is   Ŷ =   -116107.409   +   237.255   *x

revert back for doubt

thanks