Statistics tasks

An analytician is studying the profits of a company over the course of ten years. Let X be the number of years after the inital year the analytician is studying. Y is the profits in year X and the analytician believes the profits are a normal distribution stochastic(random) variable with expectation 𝐸(𝑌)=𝛽0+𝛽1𝑥 and standard deviation 𝜎=0.08. Based on these observations the analytician finds that:
𝑥¯=3.6 and 𝑦¯=4.26
𝑀=∑^9_𝑖=0 (𝑥𝑖−𝑥¯)^2=7.44,
∑^9_𝑖=0 (𝑥𝑖−𝑥¯)𝑦𝑖=4.96

(I added this as a picture too as I have a hard time writing formulas on here)


1. Estimate 𝛽0 og 𝛽1.

2. Can it be proven that the yearly increase in profits, 𝛽1, is bigger than 0.5? Formulate fitting hypothesis and do a hypothesis test at 0,5% significance level.
Critical value=
H1 or not H1?

3.Find a 99% confidence interval for expected profits for x=5
Upper confidence limit:
Lower confidence limit:

4. Find a 95% prediction interval for expected profits for x=1
Upper prediction limit:
Lower prediction limit:


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