Question

EXERCISE

1. A shop sells home computers. The numbers of computers sold in each of five successive years were as follows:

Year (x)	1	2	3	4	5
Sales (y)	10	30	70	140	170

1. Draw a scatter diagram for the data
2. Find the least squares regression line of y on x and fit it on you scatter plot
3. The shop manager uses this regression line to predict the sales in the following (i.e. the 6^th) year. Find the predicted sales.
4. Comment on the fit of this regression line and on the prediction made for the sales in the sixth year

[y=43x-45,   213]

Answer 1

.................

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	15	420	10	19120.0	430.00
mean	3.00	84.00	SSxx	SSyy	SSxy

sample size ,   n =   5          
here, x̅ = Σx / n=   3.00   ,     ȳ = Σy/n =   84.00  
                  
SSxx =    Σ(x-x̅)² =    10.0000          
SSxy=   Σ(x-x̅)(y-ȳ) =   430.0          
                  
estimated slope , ß1 = SSxy/SSxx =   430.0   /   10.000   =   43.0000
                  
intercept,   ß0 = y̅-ß1* x̄ =   -45.0000          
                  
so, regression line is   Ŷ =   -45.0000   +   43.0000   *x

..............

Predicted Y at X=   6   is                  
Ŷ =   -45.00000   +   43.000000   *   6   =   213.000

..............

based on regression line, the sales for 6 th year is predicted to be 213

.................

THANKS

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