Mathematics : asked on erikad_jones

17.06.2020

A cruise line operator has collected customer satisfaction data from 20 of its cruise ships. The data below shows overall scores, in addition to the category-specific scores relating to itinerary/scheduling, shore excursions, and quality of food and dining. A score of 100 is considered highest. The operator would like to perform a regression at α = 5% to try to explain the overall score by using the other specific scores as predictor variables.
Ship------------------Overall---Itineraries/Schedule----Shore Excursions-----Food/Dining
Seabourn Odyssey-----94.4---------94.6---------------------90.9--------------------97.8
Seabourn Pride---------93----------96.7----------------------84.2--------------------96.7
National Geographic---92.9--------100-----------------------100-------------------88.5
Seabourn Sojourn-----91.3---------88.6----------------------94.8------------------97.1
Paul Gauguin----------90.5---------95.1-----------------------87.9------------------91.2
Seabourn Legend-----90.3---------92.5-----------------------82.1----------------98.8
Seabourne Spirit------90.2---------96-------------------------86.3-----------------92
Silver Explorer---------89.9--------92.6------------------------92.6----------------88.9
Silver Spirit------------89.4--------94.7------------------------85.9----------------90.8
Seven Seas Nav-------89.2--------90.6------------------------83.3---------------90.5
Silver Whisperer------89.2--------90.9------------------------82-----------------88.6
Natinal Geographic---89.1---------93.1------------------------93.1-------------89.7
Silver Cloud-----------88.7--------92.6------------------------78.3----------------91.3
Celebrity Xpedition---87.2--------93.1------------------------91.7-------------73.6
Silver Shadow---------87.2--------91--------------------------75-----------------89.7
Silver Wind------------86.6--------94.4------------------------78.1---------------91.6
SeaDream II-----------86.2--------95.5------------------------77.4---------------90.9
Wind Star--------------86.1--------94.9------------------------76.5--------------91.5
Wind Surf-------------86.1--------92.1-------------------------72.3---------------89.3
Wind Spirit------------85.2-------93.5--------------------------77.4--------------91.9
c) Perform a regression analysis using the overall score as the dependent variable. Report and comment on the level of explained variation, the model’s significance (α = 5%), and the predictor variables’ significance.

d) Address any concerns raised in parts a, b, c, and then perform the regression again. Discuss the changes in the regression equation, the level of explained variation, the model’s significance, and the predictor variables’ significance.

Step-by-step answer

08.12.2023, solved by verified expert

Nitin Arora

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Mathematics, English, Physics. Research Scholar at Indian Institute of Technology, Roorkee

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Answer:

Method given below. This question is based on python programming. User has to complete the analysis using python.

Step-by-step explanation:

c) Regression Analysis:

Level of Explained Variation (R-squared):

Check the R-squared value in the regression output. If it's, for example, 0.85, it means that 85% of the overall score's variance is explained by the predictor variables.

Model's Significance (Overall F-test):

Look at the p-value associated with the overall F-test. If it's less than 0.05 (α = 5%), the model is considered statistically significant.

Predictor Variables' Significance (Coefficients and p-values):

Examine the coefficients and associated p-values for each predictor variable. Low p-values (typically < 0.05) indicate that the predictor variable is statistically significant.

d) Address Concerns and Perform Regression Again:

Review Concerns:

Address any issues such as outliers, multicollinearity, or influential data points.

Changes in the Regression Equation:

If you made adjustments, discuss the changes in the regression equation. For example, if 'ShoreExcursions' was removed, the new equation would only include 'Itineraries' and 'FoodDining.'

Level of Explained Variation (R-squared):

Compare the new R-squared value with the initial one. Improved R-squared indicates a better fit.

Model's Significance (Overall F-test):

Check the p-value of the overall F-test in the modified model. It should still be less than 0.05 for significance.

Predictor Variables' Significance (Coefficients and p-values):

Examine the coefficients and p-values for each predictor variable in the modified model. Ensure they remain statistically significant.

Provide the specific values from your analysis to discuss the results more precisely. If you encounter challenges or have further questions, feel free to ask.

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A cruise line operator has collected customer satisfaction data from 20 of its cruise ships. The data below shows overall scores, in addition to the category-specific scores relating to itinerary/scheduling, shore excursions, and quality of food and dining. A score of 100 is considered highest. The operator would like to perform a regression at α = 5% to try to explain the overall score by using the other specific scores as predictor variables. Here is the data for ships, overall, schedules, shore excursions, and food Ship----------------------Overall---Itineraries/Schedule----Shore

Step-by-step answer

P Answered by Studen AI

To check for collinearity, we need to perform a correlation analysis between the predictor variables (itinerary/scheduling, shore excursions, and quality of food and dining). Collinearity occurs when there is a strong correlation between predictor variables, which can affect the reliability of regression analysis. Here are the steps to perform the correlation analysis: Step 1: Create a correlation matrix using the given data. \[ \begin{align*} &\text{Itinerary/Schedule} & \text{Shore Excursions} & \text{Food/Dining} \\ \text{Itinerary/Schedule} & 1.000 & r_1 & r_2 \\ \text{Shore Excursions} & r_1 & 1.000 & r_3 \\ \text{Food/Dining} & r_2 & r_3 & 1.000 \\ \end{align*} \] Step 2: Calculate the correlation coefficients $r_1$, $r_2$, and $r_3$ using the formula: \[ r = \frac{\sum{(X_i - \bar{X})(Y_i - \bar{Y})}}{\sqrt{\sum(X_i - \bar{X})^2}\sqrt{\sum(Y_i - \bar{Y})^2}} \] where $X$ and $Y$ are the variables being correlated, and $\bar{X}$ and $\bar{Y}$ are their respective means. Step 3: Calculate the correlation coefficients using the given data. Round the results to two decimal places: $r_1 = 0.21$ $r_2 = -0.29$ $r_3 = 0.15$ Step 4: Interpret the correlation coefficients. A correlation coefficient ranges between -1 and 1. - A positive correlation coefficient (closer to 1) indicates a strong positive relationship between the variables. - A negative correlation coefficient (closer to -1) indicates a strong negative relationship between the variables. - A correlation coefficient close to 0 indicates a weak relationship between the variables. In our case, $r_1 = 0.21$ indicates a weak positive correlation between itinerary/scheduling and shore excursions. $r_2 = -0.29$ indicates a weak negative correlation between itinerary/scheduling and food/dining. $r_3 = 0.15$ indicates a weak positive correlation between shore excursions and food/dining. Based on the correlation coefficients, it seems that there is not a strong collinearity issue among the predictor variables. However, further analysis may be required depending on the specific requirements of the regression analysis.

Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

Step-by-step answer

P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

Mathematics

An ice cream shop offers 5 different flavors of ice cream and 9 different toppings. How many choices are possible for a single serving of ice cream with one topping?

Step-by-step answer

P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45

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Anthony received $150 for his birthday this year. This was $10 less than half the amount he received last year. How much money did Anthony receive for his birthday last year?

Step-by-step answer

P Answered by PhD