Question

The following data show the brand, price ($), and the overall score for 6 stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest). The estimated regression equation for these data is = 24.9 + 0.301x, where x = price ($) and y = overall score.Brand Price ScoreBose 18 76Scullcandy 150 71Koss 95 62Phillips/O'Neill 70 57Denon 70 30JVC 35 34Round your answers to three decimal places.a. Compute SST, SSR, and SSE.

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

SST = 1800

SSR = 1512.376

SSE = 287.624

b

coefficient of determination  is $r^2 \approx 0.8402$

What this is telling us is that 84.02% variation in dependent variable y can be fully explained by variation in the independent variable x

c

The correlation coefficient is   $r = 0.917$

Step-by-step explanation:

The table shown the calculated mean is shown on the second uploaded image

Let first define some term

SST (sum of squares total) : This is the difference between the noted dependent variable and the mean of this noted dependent variable

SSR(sum of squared residuals) : this can defined as a predicted shift from the actual observed values of the data  

SSE (sum of squared estimate of errors): this can be defined as the  sum of the square difference between the observed value and its mean

From the table

  $SST = SS_{yy} = 1800$

  $SSR = \frac{SS^2_{xy}}{SS_{xx}} = \frac{4755^2}{14950} = 1512.376$

  $SSE =SST-SSR$

          $=1800 - 1512.376$

           $= 287.62$

The coefficient of determination is mathematically represented as

               $r^2 = \frac{SSR}{SST}$

                    $= 1-\frac{SSE}{SST}$

                   $r^2= 1-\frac{287.6237}{1800}$

                  $r^2 \approx 0.8402$

The correlation coefficient is mathematically represented as

           $r = \pm\sqrt{r^2}$

Substituting values

            $r = \sqrt{0.84020}$

               $r = 0.917$

this value is + because the value of the coefficient of x in estimated regression equation($24.9 + 0.301x,$) is positive