Starting with the results of Correlation Analysis: r(price, weight) = 0.91 indic

Question

Starting with the results of Correlation Analysis: r(price, weight) = 0.91 indicates there's a high correlation between the price of the beef cattle and its weight. For example, more the weight of the cattle more the price it will be sold at the auction (Black, 2017). Next, (t=3.45, p<0.01) Indicates the significance of correlation to see if it's different from 0 (Ho:r=0 versus H1:r eq0). Additionally, assume significance level of 0.05 against that we want to validate our test results. Here we see that our p-value is less than 0.01 which, in turn, will be less than 0.05. Followed by, we reject our null hypothesis and conclude that our correlation that we calculated above is significantly different from zero and that there is a strong relationship between the price of the cow and the weight. However, utilizing the results of regression analysis where a mathematical relation has been built between the price of the cow and the weight. Explanation, y = 200 + 0.15x depicts the mathematical equation by which, we can predict the price of the cattle (y) which has x amount of weight. For example, if we have 500 kg of the cow (x=500), it's price will be 200+0.15*500 = 275. 200 here is the intercept term indicating that even if we do not have a cow, we get at least 200 at the auction. Followed by, R2 = 0.83 shows the percentage of variation in y, the price of the cow. Explained by the explanatory variable the weight of the cow. It ranges between 0 and 1, and a high R2 is right. Since we have a pretty high R2; we say that 83 percent of the variation in the price is explained by the weight. Meaning this model is accurate, F=15.46,p=0.001 gives the test results of the models fit. As mentioned above, at 0.05 alpha level, our model turns out significant as the p-value(=0.001)<0.05. Finally, we conclude that the above calculations in the relation between the weight of the cow and its price can be used to predict the fair market price at the auction.

In the context of the y-intercept - you are correct!. When x = 0 , the base price of a cow is $200. That means that regardless of weight, it will cost you at least $200 for each head of cattle you plan to purchase.

So, in operational terms, what does the slope of 0.15 mean?

And, based on the other parameters presented, how much in total should Big Sky budget for the auction?

Explanation / Answer

The slope of 0.15 means that for every increase of 1 in weight of the cow, the price of the cow would increase by 0.15. See example below:-

(X=1)=Y=200+0.15(1)=200+0.15=200.15

(X=2)=Y=200+0.15(2)=200+0.30=200.30

As you can see that when x increases by 1, price increases by 0.15.

The budget should be based on the weight of the cow/cows they are looking to bid for adding a fixed amount of 200 for each of the cow.

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