Question

In: Statistics and Probability

The table below shows data collected on the vessel calls for a port in Ghana, from...

The table below shows data collected on the vessel calls for a port in Ghana, from 2007-2016 to study the relationship between the number of Commercial Vessels (C.V.) and Offshore Vessels (O. V.). Year 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 C. V. (X) 527 486 481 558 623 611 606 543 615 673 O. V. (Y ) 67 129 475 719 1175 1053 758 844 910 928 Assuming a linear regression model E(Y |X = x) = α + β(x − x¯): a. Fit a regression model of the number of offshore vessels on commercial vessels, and give practical interpretation of the regression parameter estimates. [10 Marks] b. Construct a 95% confidence and prediction intervals for the number of offshore vessels corresponding to 742 commercial vessels.

Expert Solution

Create a table of all summations as below

n	Commerical Vessels (X)	Offshore Vessels (Y)	X^2	Y^2	XY
1	527	67	277729	4489	35309
2	486	129	236196	16641	62694
3	481	475	231361	225625	228475
4	558	719	311364	516961	401202
5	623	1175	388129	1380625	732025
6	611	1053	373321	1108809	643383
7	606	758	367236	574564	459348
8	543	844	294849	712336	458292
9	615	910	378225	828100	559650
10	673	928	452929	861184	624544
SUM →	5723	7058	3311339	6229334	4204922

Tabulate the values using regression parameters as below on excel

Regression Parameters	Commerical Vessels (X)	Offshore Vessels (Y)	Estimated Values	SSE
a	-1922.409	527	67	497.7659852	185559.334
b	4.59236236	486	129	309.4791286	32572.71586
		481	475	286.5173168	35525.72186
		558	719	640.1292183	6220.600207
		623	1175	938.6327715	55869.46671
		611	1053	883.5244232	28721.97113
		606	758	860.5626114	10519.08926
		543	844	571.2437829	74395.95394
		615	910	901.8938726	65.70930079
		673	928	1168.250889	57720.48983
				SUM →	487171.0521

orchestra answered 1 year ago

The data below shows data collected at the end of a statistics class to investigate the...

The data below shows data collected at the end of a statistics class to investigate the relationship between x = study time per week (average number of hours) and y = college GPA. The table shows the data for the 8 males in the class on these variables and on the number of class lectures of the course that the student reported skipping during the term. Is there a statistically significant correlation between study time and GPA at the .05...

Data collected from a sample of houses are organized and stored in the Table below. Develop...

Data collected from a sample of houses are organized and stored in the Table below. Develop a regression model that predicts the Assessed value of a house based on size of the house and presence of a fireplace (Fireplace=1. No fireplace=0). assessed value size fireplace 234.4 2 1 227.4 1.71 0 225.7 1.45 0 235.9 1.76 1 229.1 1.93 0 220.4 1.2 1 225.8 1.55 1 235.9 1.93 1 228.5 1.59 1 229.2 1.5 1 236.7 1.9 1 229.3 1.39...

The table below represents data on a variable of interest collected from a single sample. It...

The table below represents data on a variable of interest collected from a single sample. It is known that the variable of interest has a mean of 10 and a standard deviation of 5 in the general population. A researcher is interested in testing whether the population from which this sample was selected is different from the general population. Data 9 7 12 5 6 4 8 11 3 7 What are the appropriate hypotheses for this analysis? What is/are...

QUESTION The table below shows data collected over a two-hundred-year time span in a woodland area....

QUESTION The table below shows data collected over a two-hundred-year time span in a woodland area. Each year, the number of new invasive species that appeared for the very first time in that woodland was recorded. Do new invasive species appear in random years, or non-random years? If they appear randomly, the data should follow a Poisson distribution. Calculate the mean number of new invasive species per year Test whether the data fit a Poisson distribution, making sure the data...

6) The table below represents data on a variable of interest collected from a single sample...

6) The table below represents data on a variable of interest collected from a single sample measured at two different points in time. A researcher is interested in testing whether scores are higher at the second measurements. Time 1 8 6 7 5 2 8 9 3 4 7 Time 2 7 9 11 6 4 5 8 7 4 5 a) What are the appropriate hypotheses for this analysis? b) What is/are the critical value(s) for this test at a...

The table below represents data on a variable of interest collected from a single sample measured...

The table below represents data on a variable of interest collected from a single sample measured at two different points in time. A researcher is interested in testing whether scores are higher at the second measurements. Time 1: 8 6 7 5 2 8 9 3 4 7 Time 2: 7 9 11 6 4 5 8 7 4 5 a) What are the appropriate hypotheses for this analysis? b) What is/are the critical value(s) for this test at a...

The table below represents data on a variable of interest collected from two independent groups, in...

The table below represents data on a variable of interest collected from two independent groups, in which each group was randomly assigned 10 participants. A researcher is interested in testing whether the two groups have different means. Group 1 = 4, 4, 2, 6, 3, 5, 6, 1, 5, 4 Group 2 = 6, 10, 4, 7, 8, 5, 9, 10, 6, 7 Please bold answers and show work a) What are the appropriate hypothesis for this analysis? b) What...

The table below show data that has been collected from different fields from various farms in...

The table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a linear model that express Vitamin C content as a function of the weight of the Raspberries. grams Vitamin C content in mg 75 21.2 80 23.2 85 25 90 27.8 95 30 100 32.3 105 33.6 A) Find the regression equation:...

The data in the table below shows the ages of a group of people in a...

The data in the table below shows the ages of a group of people in a certain community. 47 31 42 33 58 51 25 28 62 29 65 46 51 30 43 72 73 37 29 39 53 61 52 35 a. Construct an ordered stem-and-leaf diagram to represent the above data set. b. Find the mean of the bonuses. c. Find the median of the bonuses. d. Find the mean absolute deviation. e. Find the variance and standard...

A4. The data below shows the weekly cases of Covid-19 for Ghana as at 19th June...

A4. The data below shows the weekly cases of Covid-19 for Ghana as at 19th June 2020 since the first case was recorded on 2nd March 2020(Source: WHO). 2571 1473 1582 817 956 2439 1017 920 513 263 174 72 121 11 It is being argued on public airwaves that, the average weekly cases in Ghana is more than 500. By testing the claim of what is being said on airwaves using the Sign Test, compute the significance probability of...