Question

Please show work

8.)"The Walking Dead" is an American post-apocalyptic horror drama TV series about a sheriff's deputy who awakens from a coma to find a post-apocalyptic world dominated by flesh-eating zombies. He sets out to find his family & encounters many other survivors along the way. Below are the IMDB ratings of 6 randomly selected episodes. We are interested in determining whether there is correlation between the variables (episode # & IMBD ratings) Episode Name IMBD Rating "What Lies Ahead" 7 8.5 "Cherokee Rose" 10 7.6 "Beside the Dying Fire" 19 9.2 "Welcome to the Tombs" 35 8.1 "The Grove" 49 9.2 Strangers" 53 8.7 WALKING DEAD a) Find the sample correlation coefficient & describe it using 2 adjectives discussed in class. b) Construct the null & alternative hypotheses to determine if there is correlation among the entire "The Walking Dead" series. c) Make your conclusion in the context of the problem. Explain why d) Find the equation of the best-fit line. Interpret the meanings of the slope & y-intercept in the context of the problem e) Predict the IMDB rating of "When the Dead Come Knocking" (episode #26). Then calculate the error in the prediction: the actual rating of the episode was 8.6.

Answer 1

Part a

The sample correlation coefficient between the dependent variable IMBD rating and independent variable number of episodes is given as r = 0.427074909. This means there is a considerable or intermediate positive linear relationship exists between the given two variables IMBD rating and number of episodes.

Part b

Here, we have to use t test for the population correlation coefficient. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: There is no any statistically significant correlation between the two variables IMBD ratings and number of episodes.

Alternative hypothesis: H_a: There is a statistically significant correlation between the two variables IMBD ratings and number of episodes.

Part c

We assume level of significance for this test as α = 0.05.

The test statistic formula is given as below:

t = r*sqrt(n – 2)/sqrt(1 – r^2)

We are given

n = 6

r = 0.427074909

t = 0.427074909*sqrt(6 - 2)/sqrt(1 - 0.427074909^2)

t = 0.854149818/0.904216247

t = 0.944630027

df = n – 2 = 6 – 2 = 4

P-value = 0.3983

(by using t-table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that there is a statistically significant correlation between the two variables IMBD ratings and number of episodes.

Part d

The regression model by using excel is given as below:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.427074909
R Square	0.182392978
Adjusted R Square	-0.022008778
Standard Error	0.635368765
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	0.360226131	0.360226131	0.892325885	0.398335369
Residual	4	1.614773869	0.403693467
Total	5	1.975
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	8.15879397	0.488662983	16.69615717	7.53997E-05	6.802048023	9.515539917
Episode number	0.013567839	0.014363125	0.944630026	0.398335369	-0.026310589	0.053446267

The required regression equation or line of best fit is given as below:

IMBD rating = 8.15879397 + 0.013567839*Episode number

Where,

Y-intercept = 8.15879397

Slope = 0.013567839

Y-intercept indicates that there is a 8.16 rating when no episode number is considered.

Slope of this regression line indicate that there is an increment of 0.01 approximately in the IMBD rating as there is increment of one in episode number.

Part e

We are given

Episode number = 26

IMBD rating = 8.15879397 + 0.013567839*Episode number

IMBD rating = 8.15879397 + 0.013567839*26

IMBD rating = 8.511557784

IMBD rating = 8.5 approximately

Actual rating = 8.6

Error in prediction = actual rating – predicted rating = 8.6 – 8.5 = 0.1

Error in prediction = 0.1