Question

8. Consider the relationship between the number of bids an item on eBay received and the item's selling price. The following is a sample of 5 items sold through an auction.

Price in Dollars 20 36 38 41 42

Number of Bids 5 5 5 8 8

Step 1 of 5: Calculate the sum of squared errors (SSE). Use the values b0= 2.1396 and b1= 0.1147 for the calculations. Round your answer to three decimal places.

Step 2 of 5: Calculate the estimated variance of errors, s2e. Round your answer to three decimal places.

Step 3 of 5: Calculate the estimated variance of slope, s2b1. Round your answer to three decimal places.

Step 4 of 5: Construct the 95% confidence interval for the slope. Round your answers to three decimal places.

Lower endpoint and Upper endpoint

Step 5 of 5: Construct the 90% confidence interval for the slope. Round your answers to three decimal places.

Lower endpoint and Upper endpoint

Answer 1

I used R software to solve this question.

R codes and output:

price=c(20,36,38,41,42)
> bids=c(5,5,5,8,8)
> fit=lm(bids~price)
> summary(fit)

Call:
lm(formula = bids ~ price)

Residuals:
1 2 3 4 5
0.5658 -1.2688 -1.4981 1.1579 1.0432

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.14098 3.01359 0.710 0.529
price 0.11466 0.08304 1.381   0.261

Residual standard error: 1.484 on 3 degrees of freedom
Multiple R-squared: 0.3886, Adjusted R-squared: 0.1848
F-statistic: 1.907 on 1 and 3 DF, p-value: 0.2612

> anova(fit)
Analysis of Variance Table

Response: bids
Df Sum Sq Mean Sq F value Pr(>F)
price 1 4.1966 4.1966 1.9066 0.2612
Residuals 3 6.6034 2.2011   
> sxx=sum((price-mean(price))^2)
> sxx
[1] 319.2
> confint(fit,'price',level=0.95)
2.5 % 97.5 %
price -0.149611 0.3789343
> confint(fit,'price',level=0.90)
5 % 95 %
price -0.08076338 0.3100867

Step 1

SSE = 6.603 (See ANOVA table in R output )

Step 2

Estimated variance of error = S²_e = MSE = 2.201

Step 3

Estimated variance of slope = MSE / S_xx

Where S_xx = ( X - X_bar )²

Estimated variance of slope = 2.201 / 319.2 = 0.007

Step 4

95% confidence interval for slope is

Lower endpoint = -0.150

Upper endpoint = 0.379

Step 5

90% confidence interval for slope is

Lower endpoint = -0.081

Upper endpoint = 0.310