Regression

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The business question that I am addressing is whether the price (y-intercept) of a sample of used cars (n=50) has a relationship with the independent variables miles (k), mpg, year, and engine type. The best univariate technique to predict the value of (y) is the mean, which is $26, 268. The best technique to measure the y-intercept is how many miles (k) the used car has been driven by the previous owner. This was found by measuring the strongest correlation between price and the independent variables, its absolute value was thirty-eight percent. * The estimated equation is ŷ= 112.24x+32,162

The best way to interpret this equation is for every additional used car sold at $32,162 there is a decrease of 112k in y. 14.8% of the variation of the price can be explained by the equation. This was found by checking the r-squared, which is a powerful tool in Anova; it measures how well future outcomes are likely to be predicted by the model. The reason why we do hypothesis testing is; it’s an assertion about the distribution of one or more random variables. The hypothesis test can be set up:

H0: β1 = 0 With Alpha .05
Ha: Β1 ≠ 0
Reject H0, if p value is <.05
Do not reject Ha, if p value is > or equal to .05
The p value is .006
My decision: Is to reject H0, there is a significant relationship. The predicted model for the dependent variable I got by multiplying the first miles (k) into the equation ŷ= -112.24(100,000) +32,162 which gave me -11,191, 832. This means miles are predicted to decrease by 11,191,832 when price goes up by one. There is a strong negative relationship. The independent variables will affect price of used cars differently. The miles (k) of the car are going to increase/decrease the price of the car, if the miles on the car are too high (ex: over 120,000 miles; price $9,000 also depending on brand of car). The mpg (how many miles car travels on single gallon) is going to increase/decrease sales price of the car if...
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