The data below represent a firm’s dollars spent on advertising for a sample of 4 months...

The data below represent a firm’s dollars spent on advertising for a sample of 4 months and the firm’s sales (in units sold) for those months.

month	advertising expenditures (x)	units sold (y)
1	$2215	543
2	$2975	664
3	$2150	538
4	$2060	575

1. What is the correct interpretation of the coefficient of determination?
2. What are expected sales if advertising spending is $3000?

3. What is the size of the error term for month 1?

4. Because the OLS method was used, what can be said about the fit of this line to the scatterplot of data?

Solutions

Expert Solution

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
2215	543	18225.00	1369.00	4995.00
2975	664	390625.00	7056.00	52500.00
2150	538	40000.00	1764.00	8400.00
2060	575	84100.00	25.00	1450.00

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	9400	2320	532950	10214.0	67345.00
mean	2350.00	580.00	SSxx	SSyy	SSxy

R² = (Sxy)²/(Sx.Sy) = 0.8332

interpretation : it says that 83.32% (0.8332) data is explained by the explainatory varible of X of response variable Y

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

Predicted Y at X= 3000 is
Ŷ = 283.04766 + 0.126363 * 3000 = 662.136

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

Ŷ for month 1 =562.941

residual,ei=y-yhat =-19.941

error = (Y-Ŷ)²
=397.64
............

It is good fit data..strong linear relationship

please revert back for doubt

orchestra answered 1 year ago

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