Question

In: Math

8. Consider the relationship between the number of bids an item on eBay received and the...

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

Solutions

Expert Solution

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 = S2e = MSE = 2.201

Step 3

Estimated variance of slope = MSE / Sxx

Where Sxx = ( 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


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