Use the table below to answer the final questions: It is...

Use the table below to answer the final questions: It is believed that the average numbers of hours spent studying per week (HOURS) during undergraduate education should have a positive relationship with the starting salary after graduation. Given below is the Microsoft® Excel output for predicting starting salary (Y) using number of hours spent studying per week (X) for a sample of 51 students. NOTE: Only partial output is shown. ANOVA df SS MS F Significance F Regression 1 166.542 166.542 6.12 Residual 50 1499.86 27.211 Total Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 29712.95 12628.38 2.35 0.0227 4335.28 55090.62 Hours 2193.93 886.81 2.47 0.017 411.82 3976.04 Question 22 1 pts Referring to the table above, find the estimated salary for students who study 12 hours per week. Round to the nearest hundredth (two decimal places). Note, if you feel the estimated salary is $24,892.15, then just type 24892.15. Question 23 1 pts Refer to the table above. Calculate the value of $R^2$ AND briefly interpret its meaning.

Transcript

00:01 Once again, welcome to a new problem.

00:04 This time we're dealing with regression.

00:07 We're dealing with regression.

00:08 And obviously, there are two components to regression.

00:13 The first component is correlation.

00:16 And the other component is the what you call the regression equation.

00:26 And the regression equation is connected to prediction.

00:31 What we can call hypothesis testing.

00:36 So there is hypothesis testing under prediction and your typical correlation value, the r value goes from negative 1 up until 1, where 1 is a positive perfect correlation.

00:59 And of course, negative 1 is a negative, a negative, perfect correlation.

01:12 When you think about regression, the regression equation is y hat equals to a plus bx and this is the same as saying y hat is beta not plus beta 1x and the beta not is the intercept and of course the beta 1 happens to be slope of the regression or the slope of the regression equation we're looking at a new problem and in this particular problem there's an assumption that the average number of hours for studying has a positive relationship to the starting salary so has a positive relationship to the starting salary and assuming the average number of hours of studying is x and x is the independent variable and the starting salary.

02:20 Y happens to be the dependent so this is going to be the dependent variable so r squared r squared this is the what we call the coefficient this is a coefficient of determination.

02:50 So you have a coefficient of determination that you're looking at.

02:54 We also have the adjusted r squared and multiple r.

02:59 This is the correlation coefficient that you're looking at.

03:03 And the standard error and the observation, we have the anova table, and the sum of squares is a special component of the anova table.

03:15 We have the total sum of squares sst, and we have the regression sum of squares ssr.

03:25 The other table reflects the intercept value, which is the coefficient and also the slope value.

03:36 And the first thing we want to do is we want to determine the linear regression equation.

03:42 So remember the linear regression equation.

03:46 Is the same as y hat equals to a plus bx.

03:51 A happens to be the intercept.

03:54 So that's negative 1 .8940, negative 1 .8940.

04:04 And we also have the slope.

04:07 So 0 .9795.

04:09 It's a positive slope.

04:11 So 0 .9795.

04:15 And then we also have x right there.

04:20 We also have x.

04:21 So this is the regression equation.

04:24 The second part of the problem wants us to determine to interpret, not to determine to interpret the intercept and the slope.

04:36 So the intercept will say at negative 1 .8940, the.

04:47 Intercept is the point it's the point where the graph crosses the graph crosses the y -axis so that happens at negative 1 .8940 so it means that at a zero hours studying at zero hours studying, the salary is negative...

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