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My data was collected using the population census of major cities in the United States, as well as the amount of water used in each city (g.).

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The greater the population of a city, the more water will be used.

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The purpose of this project is to prove that there is a positive correlation between population and water usage.

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City Pop. vs. Daily Water Usage (x1000 gal.)

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City Pop. vs. Daily Water Usage (x1000 gal.)

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ŷ = 76279.7294 + 0.1327x

r = 0.811

r2 = 0.658

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ŷ = 225.0349 + 53.5741x

r = 0.212

r2 = 0.045

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When analyzing the scatterplot, we can see that there is little to no correlation between the number of people in households and the number of gallons of water used in households daily. However, the Least Squares Regression Line does omit a slight positive trend. The purpose of the LSRL is to predict one variable's value based on the other's value. It's drawn in such a way that it minimizes the sum of the squared differences between the observed data points and the predicted values on the line, also known as the residual.

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In context, our Slope explains that for every additional member who lives in a household, we would expect the daily water usage to increase by 53.5741 gallons.

In context, our Y-intercept represents the number of gallons, in this case 225.0349, that are used when x = 0, or when there is no body who is living in a household.

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The number of gallons in my household was overestimated by about 54 gallons by the LSRL. The LSRL predicts that at x = 3, the number of gallons used in a household would be 385.7572 (225.0349+53.5741(3) = 385.7572), however such is not the case. My household used a bit less. A confounding variable that may affect my household's residual is the fact that we do not use sprinklers often, while other households do. Sprinkler use can be an overall confounding variable.

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In context, the r and r² values tell us the direction of the given correlation between the number of people in households and daily water usage, as well as the strength of said correlation. If an r-value is negative, there is an inverse relationship between two variables, however because our r-value is positive we can conclude that there is a slight positive relationship between the two variables. Additionally, the r² value tells us the strength of the correlation. The closer the r² value is to 1, the greater the correlation, and vice versa. However, because our r² value is super close to 0, we can conclude that there is little correlation if any concerning number of people in households and daily water usage on our small scale.

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While looking at the graph, we can see there is a moderate positive relationship between city population and daily water usage (x1000 gal.). Essentially, as the population increases, more water will be used daily in that city. Such is reaffirmed in our r and r2 values. Our r value of 0.811 displays a positive correlation between the two variables (direction) and our r2 of 0.658 displays that there is a moderate correlation between the two variables(strength). Overall, the bi-variate model displays the increase in water usage that occurs when the population of water users increases.

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I believe we can use this data to predict the water usage for our entire district, given that the district shares a similar overall demographic.

I also believe that this data can be applied to our city, given my former reasoning. However, I am unsure if the data can be applied to our state. The state of CA as a whole consists of a large variety, and thus would not share the same demographic as the demographic in our city. Demographics would vary by income, water access, and traditional family beliefs.

Using the Pop. vs Water usage LSRL (76279.7294 + 0.1327(1.5 million) we can predict that our city would use approximately 220,000 gallons a day. Similarly for our state, (76279.7294 + 0.1327(40 million) we can predict California to use approximately 5, 384,000 gallons per day. Considering California's high population, its daily water usage is most likely higher but in reason than higher states. As a whole, population and water access would be confounding variables in our data.