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You have observed the price and unit sales for your company's product over the past ten months. the data are:

price unit sales
20 797
14 879
12 901
15 851
16 835
17 850
17 798
16 802
14 853
16 833
estimate the relationship between price and unit sales (where price is the factor and unit sales is the outcome). what is the p-value for the hypothesis that the slope coefficient is zero versus not zero?

User Situee
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Final answer:

To determine the relationship between price and unit sales, a regression analysis is conducted to calculate the least-squares line. With a p-value of 0.026, we reject the null hypothesis and conclude that a significant linear relationship exists.

Step-by-step explanation:

estimate the relationship between price and unit sales:

To estimate the relationship between price and unit sales, where price is the independent variable and unit sales is the dependent variable, a scatter plot can be drawn to visualize the data. Through visual inspection or regression analysis, we can determine if a significant linear relationship exists.

Using statistical software or a calculator, we calculate the least-squares line and generate the equation in the form ลท = a + bx, where 'a' is the y-intercept and 'b' is the slope. The strength and significance of the relationship can be measured by the correlation coefficient r, and we check if 'r' significantly differs from zero.

If the hypothesis test for the slope coefficient being zero (null hypothesis) versus not zero (alternative hypothesis) renders a p-value of 0.026, which is less than the common significance level (alpha) of 0.05, we reject the null hypothesis. Consequently, we conclude that there is a significant linear relationship between price and unit sales and that the regression line can be used for predicting future sales based on price.

User Skwiggs
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