1. The graph below shows a slight positive relationship between having a higher credit balance with a larger household size. 2. The equation of best fit, also known as the regression equation, is Credit Balance($) = 2591 + 403 Size. This means that for each 1 increase in household size that that credit balance increase by $403.
3. The coefficient of correlation is the square root of .566 which is .7523. This value being closer to one than to zero and being positive implies strong linear relationship between credit balance and size. It confirms that as credit balance increases, household size will also increase.
4. The coefficient of determination is .566. This value represents the proportion of the total sample variation of y, measured by the total sum of squares of deviations in the sample from the mean, can be explained by using credit balance to predict household size. This means that 56.6% of the sample variation credit balance (y) can be explained by using household size (x) in this straight line model.
5. The null hypothesis is that Beta1equals 0 and the alternative hypothesis is that Beta1 does not equal 0. The p-value is 0.000, which is less than 0.05. Therefore, the null hypothesis that Beta1 equals zero can be rejected. There is sufficient evidence that Beta1 does not equal zero. This shows that our regression model is useful, in that credit balance does depend on household size.
6. Based on my findings, credit balance will increase by $403 per 1 unit increase in the size of the household. This is confirmed by the regression model proving to be useful and both the coefficient of correlation and coefficient of determination indicating that credit balance can be predicted by the household size.
7. We are 95% confident that the amount of increase in credit balance for every one increase in household size is between $387.31 and $419.13.