(3) The table below shows the result of a linear regression model predicting the gold medal winning height (in inches) in the men's Olympic high jump competition predicted by year (e.g. 1956, 1988, etc.). The data include 22 observations ranging from 1896 to 1992.

	estimate	standard error
intercept	-358.18	26.12
year	.23	.01

(a) In the 2016 Olympic games the winning height in the men's high jump was around 94 inches. Based on the estimates above, what would you predict would be the gold medal winning height in the men's high jump in 2016?

(b) In the 2020 Olympic games (which actually occurred in 2021 due to covid delays, but we'll treat them as if they were in 2020) the winning height in the men's high jump was just slightly over 93 inches. Based on the estimates above, what would you predict would be the gold medal winning height in the men's high jump in 2020?

(c) Conduct a formal hypothesis test at the .05 significance level of whether the true coefficient on year is equal to zero. Be sure to clearly define your null and alternative hypotheses, calculate your test statistic value, and explain what you conclude in substantive terms (i.e. what the result of this test teaches you about the relationship between year and winning high jump heights - what you learned from the results of this regression) . (Note: even though we have only 22 observations, you can assume we have a large enough number of observations so that you don't have to worry about degrees of freedom - i.e. you can use a normal distribution).

(d) Construct a 95% confidence interval for the slope coefficient on year. As above, you can assume we have a large number of observations so we don't have to worry about degrees of freedom in these calculations.

(e) If you were told that the r-squared from this regression was .93 what would that tell you about how well the men's winning height in the Olympic high jump is predicted by year?