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Introduction to inference about slope in linear regression

Introduction to sample slopes and using them to make confidence intervals or do a test about the population slope in least-squares regression .

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• Can someone please explains this to me in a way an eighth grader would get it? I am so so confused.
• Basically, what Sal is saying here is that since we don't know the true population statistics but we know the sample ( a portion from the population) statistics, we can use the sample stats to find out the population stats.

When we take many different samples, we get different regression lines () SO WE CAN ONLY ESTIMATE THE TRUE POPULATION STATISTICS AND REGRESSION LINE.

*a) Confidence interval:*
Since we don't know the actual regression line's slope, we use the sample regression line's slope to estimate it (b2). Also, because we don't know the populations actual standard deviation we use the critical value t and use the Standard Error of the statistic as we are only estimating. Therefore, the confidence interval is b2 +/- t × SE(b).

*b) Hypothesis Testing:*
The null hypothesis is that the slope of the population regression line is 0. that is Ho : B =0. So, anything other than that will be the alternate hypothesis and thus, Ha : B≠0.

This is the stuff covered in the video and I hope it helps! :)
• I think you should have chosen Shoe Size as Dependent Variable & Height as Independent Variable. So, Shoe Size should be shown on y axis.