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)

Questions:

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:

Answer

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