Question

A substance used in biological and medical research is shipped by airfreight to users in cartons of 1,000 ampules. The data in the Excel file Quiz3.xlsx (Tab Air), involving 10 shipments, were collected on the number of times the carton was transferred from one aircraft to another over the shipment route (x) and the number of ampules found to be broken upon arrival (y). Assume that the first-order regression model given below is appropriate:

y = beta0 + beta1 x + e

where e is the random error component assumed to be normally distributed with mean 0 and constant variance.

y	x
16	1
9	0
17	2
12	0
22	3
13	1
8	0
15	1
19	2
11	0

What is the estimated regression equation? Use original variables in your equation, and round your answer to 3 decimal places.

Interpret the intercept and slope.

Estimate the slope with a 95% confidence interval. Interpret your interval estimate.

What is the R-Square value? Interpret it.
What is the standard error value? Interpret it.

Answer 1

Here is the Excel output:

Estimated regression equation: y= 10.2 + 4x

Interpretation: i) Slope: with every unit increase in x, y increase by 4 units on average.

ii) Intercept: When x=0, then the estimated value of y=10.2

95% confidence interval of the slope is (2.9184, 5.0816). Interpretation: With every unit increase in x, we're 95% confident that y will increase by the above confidence interval unit on average.

R-square value = 0.901. Interpretation: 90.1% variance in y is explained by the regression line

The standard error is 1.48324. Interpretation: It tells us that how wrong the regression model is on average using the units of the response variable.