Question

In: Statistics and Probability

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

1)

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

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

2)

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

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

3)

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


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