Question

The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Price in Dollars	30	32	43	45	50
Number of Bids	2	4	5	6	7

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6 :  Determine the value of the dependent variable y^ at x=0 answer choices: b0, b1, x, y

Step 4 of 6 :  Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

Step 5 of 6 :  According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable y is given by?

Answer choices: b0, b1, x, y

6 of 6 :  Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

> x=c(30,32,43,45,50);x
[1] 30 32 43 45 50
> y=c(2,4,5,6,7);y
[1] 2 4 5 6 7
> reg=lm(y~x);reg

Call:
lm(formula = y ~ x)

Coefficients:
(Intercept) x
-3.6564 0.2114

> summary(reg)

Call:
lm(formula = y ~ x)

Residuals:
1 2 3 4 5
-0.68591 0.89128 -0.43423 0.14295 0.08591

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -3.6564 1.6582 -2.205 0.1146
x 0.2114 0.0407 5.194 0.0139 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7027 on 3 degrees of freedom
Multiple R-squared: 0.8999, Adjusted R-squared: 0.8666
F-statistic: 26.98 on 1 and 3 DF, p-value: 0.01386

#hence,

Step - 1: Slope = 0.2114

Step - 2: y - intercept =-3.6564

Step - 3: b0

Step - 4: False

Step - 5: b1

Step - 6: Coefficient of determination = 0.899