Bishop's supermarket records the actual price for consumer...

Name: Problem 43, Chapter 1: Statistics for Business and Economics: Global Edition
Uploaded: 2020-01-13T23:12:09-08:00
Duration: 7 min 23 s
Channel: Charles Carter
Description: Bishop's supermarket records the actual price for consumer food products and the weekly quantities sold. Use the data file Bishop to obtain the scatter plot for the actual price of a gallon of orange juice and the weekly quantities sold at that price. Does the scatter plot follow the pattern from economic theory?

Bishop's supermarket records the actual price for consumer food products and the weekly quantities sold. Use the data file Bishop to obtain the scatter plot for the actual price of a gallon of orange juice and the weekly quantities sold at that price. Does the scatter plot follow the pattern from economic theory?

Key Concepts

Data Analysis

Data analysis involves inspecting, cleaning, and modeling data with the goal of discovering useful information and making informed decisions. In the context of economic theory, it helps in understanding the relationship between variables like price and quantity sold by applying statistical and visual methods.

Price Elasticity of Demand

Price elasticity of demand measures how responsive the quantity demanded of a good is to a change in its price. It quantifies the degree of sensitivity and helps determine whether a change in price will lead to a proportionately larger or smaller change in demand.

Scatter Plot

A scatter plot is a graphical representation that displays individual data points for two continuous variables on a two-dimensional plane, allowing one to visually assess patterns, trends, and potential correlations between the variables. This tool is frequently used in data analysis to check for linear or nonlinear relationships.

Law of Demand

The law of demand is a fundamental principle in economics which posits that, ceteris paribus, there is an inverse relationship between the price of a good and the quantity demanded. That is, as the price increases, the quantity demanded tends to decrease, and vice versa.

Transcript

00:01 Okay, so this problem's got several parts.

00:03 So for part a it wants us to solve a system of equations.

00:06 It looks rather difficult, but we have 3 .0b plus 3 .7a is equal to 105 .0.

00:23 And for the second part, we have 3 .7b plus 4 .69a, equally 123 .9.

00:35 And it wants us to solve this because it says in solving it.

00:39 It will give us what we need for a linear regression model of a x plus b to find a line of best fit for the data given in the table.

00:49 So in order to solve this, i'm going to multiply my top equation, i think, by 3 .7.

00:57 My bottom equation by 3 .0.

01:02 And that's just to give my coefficients equal on my b values, and then we'll just subtract the equations.

01:07 So multiplying three will have 11 .1b.

01:14 We'll have 13 .69a and that's going to be equal to 388 .5.

01:35 Oof.

01:36 Now we're multiplying by 3 .7 on the top equation.

01:39 Now the bottom equation, same thing, we're going to multiply by 3 this time.

01:43 So we have 11 .1b.

01:45 So you can see that our bs are going to cancel out.

01:49 And again, multiplying by 3 is going to give us 14 .07.

01:55 It's going to give us a negative slope, which is what you would expect looking at a table like that, where the x is going up while the y is going down.

02:02 And it's going to give us 371 .7.

02:09 So if we subtract those, let's see, we're going to have negative 0 .38a equals 16 .8.

02:33 Divide both sides about negative 0 .38, and we will have a is equal to negative 44 .2105.

02:49 Looks like we just have a non -repeating decimal.

02:55 Actually, i guess it will repeat at some point, or it'll end at some point, just because this is a rational number.

03:04 Okay, so a is going to be equal negative 44 .21 or so.

03:09 Now if we plug that back in to our formula to solve for b, we can get 3 .7b plus 4 .69.

03:24 And since i have a calculator, we're just going to store that number in for a.

03:30 So this is just my answer to the last thing i did on the calculator equals 123.

03:38 I'm using the second equation for this.

03:41 Okay, plugging that in and subtracting from both sides, it's going to give me that b, and then dividing by 3 .7.

03:50 It's going to be 89 .526 and so on and so on...

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