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I would appreciate help with how to find a connection between a statement and a summary() function on linear regression model in R.

I have created a model for simple linear regression in Rstudio over data that contains data on the deviation of the earth's average temperature during the period 1970–2007 and when using summary() to this I get the following:

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And I would now like to find the connection between this model and the following statement "The greenhouse effect is not a problem, there is no proven trend towards a warmer climate". But how should I interpret the information provided by the model?

The exact question is as follows: What is the link between the statement and the model that was adapted to the same time period? It is also said that this link will lead me to which test I should use to conduct a hypothesis test on this.

My thoughts: Pr(>|t|) from what I understand gives us the p-value for two-sided testing of the null-hypotheses that no difference / change occurs (i.e. $\alpha=0$ and $\beta=0$) and since this is incredibly small, the null hypothesis should be rejected, but that is a contradiction to the statement and not a connection? And also, how can the intercept be -33 and what does this mean?

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I am not sure what you mean with "connection".

The t-test tells you the probability of observing a coefficient for year as extreme as 0.017 under the assumption that the true beta is 0. As the probability is extremely small, we can conclude that the true beta is not 0 and therefore there is a true increase in temperature described by year.

The coefficient of year tells you the estimated change of Y given a unit change in year.

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  • $\begingroup$ The exact question is "What is the link between the statement and the model that was adapted to the same time period?" with the time period being the year 1970-2007. And like you, I also interpreted it as that there is a true increase in temperature, but got a little confused since contradicts the statement and is not a link. $\endgroup$
    – user346623
    Commented Jan 13, 2022 at 16:17
  • $\begingroup$ Well, the statement is simply wrong? $\endgroup$
    – Felix Phl
    Commented Jan 13, 2022 at 16:18
  • $\begingroup$ Ok thank you! But what is the meaning of the intercept being -33? Maybe that has something to do with the link $\endgroup$
    – user346623
    Commented Jan 13, 2022 at 16:58
  • $\begingroup$ @user346623 not at all. The intercept is simply the estimate of Y when year = 0. That is of course meaningless with the data you are using as there is no linear temperature increase from year 0 to year 2007. You can instead get a meaningful intercept if you replace the actual values of year with values of 0,1,2,3 ... then your intercept will be the estimated temperature at year 0, which is in your case 1970. The slope will remain the same. $\endgroup$
    – Felix Phl
    Commented Jan 13, 2022 at 17:02
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    $\begingroup$ Thanks for the clear answer! I now understand a little bit more and can also draw the conclusion that the statement is wrong. $\endgroup$
    – user346623
    Commented Jan 13, 2022 at 17:08

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