It is argued that less time spent on social media will result in improved course marks among ECO242 students. To test whether this is the case you collect data from 20 students on their final marks (Y) and number of Instagram posts during the semester (X). You make the following calculations:∑XY=32191∑X2=34282∑X=690∑Y=1164Next, you run the following regression:marks=β^1+β^2Instagramwhere 'marks' is the final mark for the course in percentage points, and 'Instagram' is the average number of minutes per day spent on the Instagram App during the semester. Answer the remaining questions based on your results. Question 1The value for the slope parameter is? Question 2 CThe value for the intercept parameter is? Question 3 .If the standard error for the intercept parameter estimate is 1.216716, construct a 95% confidence interval for the parameter. Pr( ? ≤β1≤ ?. )=95% Question 4 .If the standard error for the slope parameter estimate is 0.129308, construct a 95% confidence interval for the parameter. Pr( ?β2≤ ?. )=95% Question 5 Assuming all else is held constant, the estimated slope coefficient above can be considered an `effect size' for Instagram post on marks. That is, for every additional Instagram post, on average, the final mark changes by β^2. You conduct a hypothesis test to see whether the estimated effect that `time spend on Instagram' has on marks is statistically significant (make use of the standard errors given above). You start out with the following null and alternative hypotheses:H0:β2=0H1:β2<0What is the calculated test statistic for this test? Question 6 Next you need to find the critical value. You decide on α=0.05. What is the critical value for this test? Question 7 Given your answers above, you conclude that... A. We reject the null hypothesis because the coefficient equals 2, which is positive. Therefore we conclude that time spent on Instagram is, on average, associated with higher marks for the course. B. The null is not rejected since the test statistic is smaller than the critical value and lies within the acceptance region of the sampling distribution. C. The null is accepted since the test statistic is larger than the critical value and lies within the acceptance region of the sampling distribution. Thus we conclude that time spent on Instagram has, on average, a positive effect - greater than zero - on the final mark for the course. D. The null is rejected since the test statistic is smaller than the critical value and lies within the rejection region of the sampling distribution. You therefore conclude that time spent on Instagram is associated with lower marks among ECO242 students. E. The null is rejected since the test statistic is larger than the critical value and lies within the rejection region of the sampling distribution. Thus we conclude that time spent on Instagram has, on average, a positive effect - greater than zero - on the final mark for the course.Question 8 .If the total sum of squares is 6058, the residual sum of squares is 163. What is the value of r2? Question 9 How would you interpret your result above (the value determined for r2? A. Variation in the final marks for the course explains a significant proportion of the variation in the amount of time spent on Instagram among ECO242 students. B. The variation in the final marks for the course does not explain much of the variation in the amount of time spent on Instagram among ECO242 students. C. The variation in the amount of time spent on Instagram among ECO242 students explains a significant proportion of the variation in final marks for the course. D. The variation in the amount of time spent on Instagram among ECO242 students does not explain much of the variation in final marks for the course.

Formulae: 1) intercept parameter= ∑Y-b∑Xn 2)slope parameter=…

Answered: Question 8 .If the total sum of…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 2AGP

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It is argued that less time spent on social media will result in improved course marks among ECO242 students. To test whether this is the case you collect data from 20 students on their final marks (Y) and number of Instagram posts during the semester (X). You make the following calculations:

∑XY=32191
∑X2=34282
∑X=690
∑Y=1164

Next, you run the following regression:

marks=β^1+β^2Instagram

where 'marks' is the final mark for the course in percentage points, and 'Instagram' is the average number of minutes per day spent on the Instagram App during the semester. Answer the remaining questions based on your results.

Question 1

The value for the slope parameter is?

Question 2

CThe value for the intercept parameter is?

Question 3

.If the standard error for the intercept parameter estimate is 1.216716, construct a 95% confidence interval for the parameter. Pr( ? ≤β1≤ ?. )=95%

Question 4

.If the standard error for the slope parameter estimate is 0.129308, construct a 95% confidence interval for the parameter. Pr( ?β2≤ ?. )=95%

Question 5

Assuming all else is held constant, the estimated slope coefficient above can be considered an `effect size' for Instagram post on marks. That is, for every additional Instagram post, on average, the final mark changes by β^2. You conduct a hypothesis test to see whether the estimated effect that `time spend on Instagram' has on marks is statistically significant (make use of the standard errors given above). You start out with the following null and alternative hypotheses:

H0:β2=0H1:β2<0

What is the calculated test statistic for this test?

Question 6

Next you need to find the critical value. You decide on α=0.05. What is the critical value for this test?

Question 7

Given your answers above, you conclude that...

A. We reject the null hypothesis because the coefficient equals 2, which is positive. Therefore we conclude that time spent on Instagram is, on average, associated with higher marks for the course.
B. The null is not rejected since the test statistic is smaller than the critical value and lies within the acceptance region of the sampling distribution.
C. The null is accepted since the test statistic is larger than the critical value and lies within the acceptance region of the sampling distribution. Thus we conclude that time spent on Instagram has, on average, a positive effect - greater than zero - on the final mark for the course.
D. The null is rejected since the test statistic is smaller than the critical value and lies within the rejection region of the sampling distribution. You therefore conclude that time spent on Instagram is associated with lower marks among ECO242 students.
E. The null is rejected since the test statistic is larger than the critical value and lies within the rejection region of the sampling distribution. Thus we conclude that time spent on Instagram has, on average, a positive effect - greater than zero - on the final mark for the course.

Question 8

.If the total sum of squares is 6058, the residual sum of squares is 163. What is the value of r2?

Question 9

How would you interpret your result above (the value determined for r2?

A. Variation in the final marks for the course explains a significant proportion of the variation in the amount of time spent on Instagram among ECO242 students.
B. The variation in the final marks for the course does not explain much of the variation in the amount of time spent on Instagram among ECO242 students.
C. The variation in the amount of time spent on Instagram among ECO242 students explains a significant proportion of the variation in final marks for the course.
D. The variation in the amount of time spent on Instagram among ECO242 students does not explain much of the variation in final marks for the course.

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