Question

Question 10 - of 17 Step 6 of 6 00:43:59 The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, ġ = bo +bix for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant Hours Unsupervised 0.5 1.5 2.5 4.5 5 Overall Grades 94 86 84 81 79 73 62 نما 4 Table Copy Data Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

Solution Question 10 From the provided information, let Xe Houve ensupervi -Sed and y = Overall grade. So then the itable. Х Y X2 y? Xoy .47 0.5 94 0.25 8836 7396 1.5 86 1a9 2.25 6.25 2.5 7056 84. 81 3 210 243 316 9 6561 4 79 16 6241 5329 4.5 73 328.5 20. a5 5 62 310 25 3844 {y² = 45263 EX-21 EY= 559 Exy = 1583.5 Ex? 79 Correlation coefficient, Y = SSxy (SSxx SSxy Exy - Ls (8 x) Eyl] where SSxy 1583.5- Ent (Q1)(559) 1583.5- 1677 SSxY = -93.5 G wbere. SSxx Ex2 - [(Ex)?] 79 (20)

99- 63 SSXX 16 Where $Syy.= Iy2-C (3x)? 45363.- [ (55912] 45263 - 44640.14286 622.8571 Y = - 93.5 16 x 623.857 - 93.5 99.82842424 -0.936607 n -0.937 Step 60f6: Co-efficient of determination, R= (v2? R? (2.937)? = 0.877969 ✓ 0.878 Therefore coeffierent of Defermination is 0.878.