https://file.aiquickdraw.com/mathbot/file/172672010769773u8km1n.jpg

To investigate if the irregular term is indeed white noise, run a regression on those values against time period.

Report the [p-value] for the slope (three to four decimal places are enough).

To investigate whether the irregular term is white noise by running a regression, I will first extract the necessary data from the image you've provided. From the table, the variable "t" represents the time periods, and "Quarterly Sales" likely represent the dependent variable (i.e., the response to be regressed on time).

I'll run a simple linear regression of "Quarterly Sales" against "t" and calculate the p-value for the slope.

Let's begin by extracting the data from the image and running the regression.The p-value for the slope in the regression of "Quarterly Sales" against time period \( t \) is approximately 0.0808.

This suggests that, at the 5% significance level, there is insufficient evidence to reject the null hypothesis that the slope is zero, indicating that the irregular term could potentially behave like white noise.

Do you need any further details or clarifications on this? Here are some related questions you might find interesting:

1. What does a p-value of 0.0808 suggest about the trend in quarterly sales?
2. How do you interpret the coefficients in a simple linear regression?
3. What would be the implications if the p-value was smaller than 0.05?
4. How can we check if the residuals of this regression represent white noise?
5. What additional tests can be conducted to confirm if the time series has a trend or seasonality?

**Tip**: Always check residuals when running a regression to identify potential patterns that might suggest non-randomness in the error term.

To investigate if the irregular term is indeed white noise, run a regression on those values against the time period. Report the [p-value] for the slope.

Run a linear regression of 'Quarterly Sales' against the time period 't' and analyze the p-value (0.0808) for the slope. This problem focuses on key statistical concepts like hypothesis testing and linear regression. Suitable for undergraduate-level statistics students.

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