Question

Assignment 22 CORECASTING PROFITS IN SUPERMARKETS A company wishes to my wishes to predict profit Y in thousands of dollars) for supermarkets with riables of total sales in thousands of dollars) of (0) Xi - foods and independent variables m nonfoods. The data are: Store Number SALES OF NONFOODS 2 3 Y PROFIT SALES OF FOOD (thousands of dollars) (thousands of dollars) 20 3050 151300 17 1890 9 1750 16 1010 27 2690 35 4210 7 1 950 2 2 2820 23 2030 5 (thousands of dollars) 350 980 830 760 930 770 440 570 310 920 6 7 8 9 10 The correlation matrix for these 3 variables is: .760 - 286 -.764 X 1. The estimated regression line relating profit, Y to food sales, X, is Y = 3.88 +0.0067 X The computed statistic is 10.95 and the standard deviation of the residuals is 5.72. Is the linear regression relationship significant at the a=0.05 significance level? Compute and interpret the coefficient of determination

please help with this problem, given the data above!

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	22700	191	7954200	618.9	53330.00
mean	2270.00	19.10	SSxx	SSyy	SSxy

sample size ,   n =   10          
here, x̅ = Σx / n=   2270.00   ,     ȳ = Σy/n =   19.10  
                  
SSxx =    Σ(x-x̅)² =    7954200.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   53330.0          
                  
estimated slope , ß1 = SSxy/SSxx =   53330.0   /   7954200.000   =   0.0067
                  
intercept,   ß0 = y̅-ß1* x̄ =   3.8805          
                  
so, regression line is   Ŷ =   3.88 +   0.0067   *x

SSE=   (SSxx * SSyy - SS²xy)/SSxx =    261.342  
          
std error ,Se =    √(SSE/(n-2)) =    5.716  
          
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.7601  
          
Coefficient of determination= R² =    (Sxy)²/(Sx.Sy) =    0.5777  

It means that 57.77% of the variation in Y can be explained by X1.

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variation	SS	df	MS	F-stat	p-value
regression	357.558	1	357.558	10.95	0.0107
error,	261.342	8	32.668
total	618.900	9

P value <0.05 , means hypthesis is significant.

Thanks in advance!

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