Multiple Linear RegressionWhat is the null and alternative hypotheses for an overall significance test if the research agency uses multiple linear regression to predict the bill amount of a credit card user using the annual income, annual credit card charges, and household size for a sample of credit card users?H0: All the regression coefficients of the household size, annual income, and annual credit card charges are equal to zero.Ha: At least one of the regression coefficients of the household size, annual income, and annual credit card charges is non-zero.H0: All the regression coefficients of the household size, annual income, and annual credit card charges are equal to zero.Ha: All the coefficients of the household size, annual income, and annual credit card charges are non-zero.H0: At least one of the regression coefficients of the household size, annual income, and annual credit card charges is equal to zero.Ha: All the coefficients of the household size, annual income, and annual credit card charges are non-zero.✕ IncorrectFeedback:The hypothesis for the overall significance test is — H0: None of the independent variables has a significant influence on the dependent variableHa: At least one independent variable has a significant influence on the dependent variable.H0: At least one of the regression coefficients of the household size, annual income, and annual credit card charges is equal to zero.Ha: At least one of the coefficients of the household size, annual income, and annual credit card charges is non-zero.

Multiple Linear RegressionIf the p-value for the overall significance hypothesis test of multiple linear regression is 0.04, what can you comment on the null hypothesis at a 99 percent confidence level?The annual income has a significant influence on the credit card bill.The annual income and annual credit card charges have a significant influence on the credit card bill.The annual income, annual credit card charges, and household size have no significant influence on the credit card bill.At least one of the annual income, annual credit card charges, and household size has a significant influence on the credit card bill.Can’t comment at a 99 percent confidence level.

Formulate the null and alternative hypotheses for simple linear regression?

In order to determine whether the coefficient in a simple linear regression model is significant or not, which null hypothesis do we propose?β0=0β0≠0β1=0β1≠0

For a sample of 30 Australian cities, a sociologist studies the crime rate in each city (crime per 100,000 residents) as a function of its poverty rate (in %) and its average income (in $1,000). A portion of the regression results shows that the coefficients for poverty and average income are 54.22 and 5.10, respectively. Based on this information, what statistical decision should be made when testing the null hypothesis that X1 has no significant effect on Y at the 1% level of significance? Assume the standard error of the slope of Y with variable X1 equals 20.50. Note: Y = crime rate in each city (crime per 100,000 residents); X1 = poverty rate (in %); and X2 = average income (in $1,000). a. Do not reject the null hypothesis. b. Accept the alternative hypothesis. c. Accept the null hypothesis. d. Reject the null hypothesis.

Suppose also that in this economy of inflation, researchers are concerned that consumers are spending less. In previous years, the mean monthly spending was $525. Provide a separate analysis to determine at the 0.10 significance level, if the mean amount spent per month significantly decreased this year. This is a one-sample mean test. Please provide: (8 points)1) The null and alternative hypotheses indicating whether it is a one or two-sided test.2) Use Data analysis and descriptive statistics to obtain the necessary summary statistics to perform this analysis. Clean up the output and copy and paste the clean output below.3) Calculate the appropriate Test Statistic showing your work which should include the point estimate and its standard error. Either copy and paste your calculations in Excel or show your hand calculations.4) Compare either the p-value to the level of significance OR your test statistic to the proper critical value and make the necessary conclusion.5) a concluding statement reporting the results of the test and the proper decisions that follow from the analysis in the context of the data.