a. Complete the missing entries from A to H in this output b. Estimate the annual credit card charges for a three-person household with an annual income of $40,000. C. Did the estimated regression equation provide a good fit to the data? Explain
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Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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- Dex Research Limited conducted a research to investigate consumer characteristics that can be used topredict the amount charged by credit card users. The following multiple regression output is based on adata collected by this research company on annual income, household size and annual credit cardcharges for a sample if 50 consumers. aComplete the missing entries from A to H in this output b. Estimate the annual credit card charges for a three-person household with an annual incomeof $40,000. c. Did the estimated regression equation provide a good fit to the data? ExplainDex Research Limited conducted a research to investigate consumer characteristics that can be used topredict the amount charged by credit card users. The following multiple regression output is based on adata collected by this research company on annual income, household size and annual credit cardcharges for a sample if 50 consumers.Regression StatisticsMultiple R 0.9086R Square AAdjusted R Square 0.8181Standard Error 398.0910Observations B ANOVA df SS MS F Significance FRegression 2 D E G 1.50876E-18Residual C 7448393.148 FTotal 49 42699148.82 Coefficients Standard Error t Stat…What is solution of following question? Dex Research Limited conducted a research to investigate consumer characteristics that can be used topredict the amount charged by credit card users. The following multiple regression output is based on adata collected by this research company on annual income, household size and annual credit cardcharges for a sample if 50 consumers.Regression StatisticsMultiple R 0.9086R Square AAdjusted R Square 0.8181Standard Error 398.0910Observations B ANOVA df SS MS F Significance FRegression 2 D E G 1.50876E-18Residual C 7448393.148 FTotal 49 42699148.82 Coefficients Standard…
- Suppose the following data were collected from a sample of 15 houses relating selling price to square footage and the architectural style of the house. Use statistical software to find the following regression equation: PRICEi=b0+b1SQFTi+b2COLONIALi+b3RANCHi+ei . Is there enough evidence to support the claim that on average, houses that are ranch style have lower selling prices than houses that are Victorian style at the 0.05 level of significance? If yes, write the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."Selling Price Square Footage Colonial (1 if house is Colonial style, 0 otherwise) Ranch (1 if house is Ranch style, 0 otherwise) Victorian (1 if house is Victorian style, 0 otherwise) 377640 1941 1 0 0 460996 3397 0 1 0 405781 2764 0 0 1 407216 2906 0 0 1 435139 3401 1 0 0 405275 2600 0 0 1 381141 2203 0 1 0 370490 2046 1 0 0 404070 2210 0 0 1 460196 3692 0 1 0 382780 2172 1 0 0 406466 2606 0 1…A study is conducted to determine if there is a relationship between the two variables, blood haemoglobin (Hb) levels and packed cell volumes (PCV) in the female population. A simple linear regression analysis was performed using SPSS. Based on the SPSS output of the ANOVA table, which of the following statements is the CORRECT interpretation? 1. The regression model statistically significantly predicts the blood haemoglobin level. 2. About 39.98 % of variance in Hb is explained by PCV. 3. The regression model does not fit the data. 4. There is significant contribution of Hb towards PCV.Would someone familiar with SPSS be able to help me complete the table and the questions? (a) Explain which of the variables have statistically significant effects at the α = 0.05 level. (b) Are the conclusions different to the results obtained by univariate regression? Explain why and which approach is likely to be preferable?
- The accompanying technology output was obtained by using the paired data consisting of foot lengths (cm) and heights (cm) of a sample of 40 people. Along with the paired sample data, the technology was also given a foot length of 14.5 cm to be used for predicting height. The technology found that there is a linear correlation between height and foot length. If someone has a foot length of 14.5 cm, what is the single value that is the best-predicted height for that person? The regression equation is Height=64.8+5.70 Foot Length Predictor Coef SE Coef T P Constant 64.79 11.98 5.41 0.000 Foot Length 5.7004 0.4126 13.82 0.000 S=5.50488 R-Sq=70.6% R-Sq(adj)=69.8% Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 147.446 1.796 (143.130, 151.762) (135.900, 158.992) Values of Predictors for New Observations New Obs Foot Length 1 14.5…A rural state wants to encourage high school graduates to continue their education and attend college. The state collected information on a random sample of high school seniors from across the state 7 years ago and is now observing how many years of education they completed. They believe students decide to achieve more education when they are more capable, have easier access to college education, and the opportunity cost of attending are lower. To explore the factors that affect the years of education completed they have used multiple regression to estimate the years of completed education as a function of: Unemployment rate - the unemployment rate in the county (3.9 – 16.8) County Hr Wage - average starting hourly manufacturing wage in the county Test - student score on college admission test (0 to 100 scale) Dist to college - Distance to near college (measured in 100’s of miles) Tuition - Tuition charged at nearest state university (measured in $1000s)…A rural state wants to encourage high school graduates to continue their education and attend college. The state collected information on a random sample of high school seniors from across the state 7 years ago and is now observing how many years of education they completed. They believe students decide to achieve more education when they are more capable, have easier access to college education, and the opportunity cost of attending are lower. To explore the factors that affect the years of education completed they have used multiple regression to estimate the years of completed education as a function of: Unemployment rate - the unemployment rate in the county (3.9 – 16.8) County Hr Wage - average starting hourly manufacturing wage in the county Test - student score on college admission test (0 to 100 scale) Dist to college - Distance to near college (measured in 100’s of miles) Tuition - Tuition charged at nearest state university (measured in $1000s)…
- A rural state wants to encourage high school graduates to continue their education and attend college. The state collected information on a random sample of high school seniors from across the state 7 years ago and is now observing how many years of education they completed. They believe students decide to achieve more education when they are more capable, have easier access to college education, and the opportunity cost of attending are lower. To explore the factors that affect the years of education completed they have used multiple regression to estimate the years of completed education as a function of: Unemployment rate - the unemployment rate in the county (3.9 – 16.8) County Hr Wage - average starting hourly manufacturing wage in the county Test - student score on college admission test (0 to 100 scale) Dist to college - Distance to near college (measured in 100’s of miles) Tuition - Tuition charged at nearest state university (measured in $1000s)…A rural state wants to encourage high school graduates to continue their education and attend college. The state collected information on a random sample of high school seniors from across the state 7 years ago and is now observing how many years of education they completed. They believe students decide to achieve more education when they are more capable, have easier access to college education, and the opportunity cost of attending are lower. To explore the factors that affect the years of education completed they have used multiple regression to estimate the years of completed education as a function of: Unemployment rate - the unemployment rate in the county (3.9 – 16.8) County Hr Wage - average starting hourly manufacturing wage in the county Test - student score on college admission test (0 to 100 scale) Dist to college - Distance to near college (measured in 100’s of miles) Tuition - Tuition charged at nearest state university (measured in $1000s)…A research department of an American automobile company wants to develop a model topredict gasoline mileage (measured in MPG) of the company’s vehicles by using theirhorsepower and weights (measured in pounds). To do this, it took a random sample of 50vehicles to perform a regression analysis as follows: SUMMARYOUTPUTRegression StatisticsMultiple R 0.865689R Square 0.749417Adjusted RSquare 0.738754Standard Error 4.176602Observations 50ANOVAdf SS MS FRegression a 2451.973702 1225.987 dResidual b 819.8680976 cTotal 49 3271.8418CoefficientsStandardError t StatIntercept 58.15708 2.658248208 21.87797Horsepower -0.11753 0.032643428 -3.60028Weight -0.00687 0.001401173 -4.90349(a) State the multiple regression equation. Interpret the meanings of the coefficients forhorsepower and weight.(b) Test the validity of this multiple regression equation at the significance level of 1%. Showyour reasoning.(c) The research department claims that the weight of the vehicle is negatively linearly related…