Question

Please answer the following questions using the formula for a and b, thank you!

Question 1: A study is conducted to examine the influence of screen time on student performance on Satis exams A class of 12 students is observed over a period of time, with the independenta le being the we amount of time per day each student spends on TV internet, and the dependent able being their subsequent Statistics eum score, in The data is shown in the belon Student HryDay Watching TV or on Exam Score alelele come to X hesday spent (1) Determine the equation of the line of best fit, relating Y = exam watching TV or on the internet. (t) Use the line of best fit calculated in Part(a) to calculate an estimate for the cum score that det would get to the nearest if they spent an average of 25 hrs/day watching TV o n the intemet Repeat for an estimate of the cam score that would resultater she spent of 5.0 hes/day watching TV or on the intemet Por the www data from the table on an-graph, and then draw the line of best fit showing at least 2 calculated points that are on that line (Hint your answers for Parts a nd be provide you with such (d) What is the predicted exam score, to the nearest for a student who completely was the TV internet Repeat for a predicted esam score for a student who spends me of 120 hesday watching TV or on the internet. Comment briefly on your answers for these two times, and what it implies about the limitations of the lincare modd e d in Part (c) Calculate the covariance between X and Y Calculate the correlation coefficient for this dataset. Calculate the coefficient of determination for this dataset, and explain what is a means with respect to the line of best fit calculated in Part) (1) Conducta hypothesis test on the significance of comcation between his/depot watching TV or on the internet, and exam performance, using the critical value method a LOC = 99% Use the p-value method to determine the comman values of LOC off which wurde in Parth) would be that there is no significant correlation between X and Y and the common LOC values (if any) for which the opposite decision would be made.

Answer 1

Answer:

a)

X.X 0 21.16 6.25 51.84 9 Xor 0 363.4 162.5 1872 123 366.6 394.8 202.8 111.8 327.6 184.8 244 8.6 15.21 17.64 15.21 73.96 15.21 7.84 16 2.8 4.0

ΣΧ = 48.6, ΣΥ = 775, ΣΧ.Υ = 2668.5, ΣΧ? = 249.32 ΣΥΣΧ? - ΣΧ. ΣΧΥ 775 - 249.32 – 48.6 - 2668.5 2 x 100.867 η-ΣΧ? - (Σ Χ)? 12 - 249.32 – 48.62 η.Σ ΧΥ – ΣΧ.ΣΥ 12 - 2668.5 – 48.6 - 775 η-ΣΧ? - (Σ Χ)? 12 - 249.32 – (48.6? , 6= 28 -8.959 9 = α + 6. y = 100.867 - 8.959 - 1

b) If a student spent 25 hilday for TV. & Internet then the predicted Score will Y = 100*867-8.959.8 = 101-8.96*2.5 asif 78.6% spent 5 has la Y = 101-8.96x5 = 101-4418 Nogt = 56.2
c)

120 100 80 60- 40 20 7 C -2 0 2 4 6 8 10 12

d) The predicted Exam Score of the student when completely not used the TV & internet houss (le x=0) is ystal arou o ao Now if we take x= 12 hrs/day wall hbo Copos Corto = 101-8.98 xize up (o) sono costol-107.52 mil 5-6.82% oboro which is not possible] The main limits occur with this model is That 7 of Scam SOR will be negative if we increases the his spent in T. 8 internet is not possible

ie, If the spending hours is more than 12 has Exactly & it does not hold good t o a) Cu(x, y) = (x-7) Lyi-y) = - 42.63- 9) 8 8 0 -0.106 f) The correlation Coefficient ra Concasy) 2724 Correlation of determination z = (-0.706) 2 MAR bolibor at = 0.498 boy son plano noog (0 ) as the efficient of determination of given fit we get 0.5 we can condode the titled Equation are more Cor) less Now the that goodl. -

g)

X Y 0 9 XY XX Y.Y 0 10000 363.4 21.16 6241 162.5 6.25 4225 187.2 51.84 676 123 1681 366.6 15.21 8836 394.8 17.64 8836 202.8 15.21 2704 111.8 73.96 169 327.6 15.21 7056 184.8 7.84 4356 244 3721 16

ΣΧ= 48.6, ΣΥ= 775, ΣΧ.Υ = 2668.5, Σx? = 249.32, ΣΥ? = 58501 η ΣΧΥ - ΣΧΣΥ τη ΣΧ? - (ΣΧ)?] - [nΣΥ? - (ΣΥ] 12 - 2668.5 – 48.6 - 775 = -0.7061 [12 - 249.32 – 48.63] - [12 - 58501 - 775]