The owner of a movie theater company would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Use α = 0.01 to test the hypotheses H0: β1 = β2 = 0 Ha: β1 and/or β2 is not equal to zero for the model  y = β0 + β1x1 + β2x2 + ε,  where x1  =  television advertising ($1,000s) x2  =  newspaper advertising ($1,000s). Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.

The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 13 varieties of Kellogg's cereal. Sugar (grams) 4. 15 12 11 8. 8 14 20 13 Calories 140 200 150 110 140 80 200 100 120 190 || 190 110 120 %3D The predictive regression equation of the number of calories on the amount of sugar is y = 97.555 + 4.730x, where x is amount of sugar (in grams) and y is calories. Estimate the calorie count for a cereal with 54 grams of sugar per serving. Round your answer to the nearest integer. calories

A mortgage is a type of loan that can be used to purchase a house. A large bank is interested in the relationship between a customers’ years of experience in their current job and the mortgage amount for customers with a mortgage. They selected 100 customers with a mortgage at random and used the data to test the claim that there is a negative linear relationship between years of experience in the current job and mortgage amount. The following hypotheses were used to test the claim. H0:β1=0Ha:β1<0 The test yielded a t-value of −3.865 with a corresponding p-value of 0.0001. Which of the following is the correct interpretation of the p-value?     If the alternative hypothesis is true, the probability of observing a test statistic of −3.865 or smaller is 0.0001. A If the alternative hypothesis is true, the probability of observing a test statistic of −3.865 or greater is 0.0001. B If the null hypothesis is true, the probability of observing a test statistic of…

Let Y = β0 + β1x + E be the simple linear regression model. What is the interpretation of the least squares estimate for β0? Select one: a. It is an estimate of the expected value of the response variable Y when the explanatory variable X is zero. b. It is an estimate of the change in the expected value of the explanatory variable X for every unit increase in the response variable Y. c. It is an estimate of the change in the expected value of the response variable Y for every unit increase in the explanatory variable X. d. It is an estimate of the expected value of the explanatory variable X when the response variable Y is zero.

You run a regression analysis on a bivariate set of data (n=21n=21). You obtain the regression equationy=0.402x+19.831y=0.402x+19.831with a correlation coefficient of r=0.916r=0.916 (which is significant at α=0.01α=0.01). You want to predict what value (on average) for the explanatory variable will give you a value of 120 on the response variable.What is the predicted explanatory value?x

7. Find slop of a linear regression model for the following data: x = [1, 2, 3, 4, 5, 6, 7] z = [ 1.40, 3.78, 4.41, 4.60, 8.40, 8.64, 12.81]. -1.7 -0.5 0.5 O 1.7 CS Scanned with CamScannel

The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.1 6.7 3.3 2.7 2.3 2.2 0.3 yy 13.8 10.7 9.9 6.6 6.1 5.9 6.1 4.5 xx = thousands of automatic weaponsyy = murders per 100,000 residents Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places)   A) How many murders per 100,000 residents can be expected in a state with 6.4 thousand automatic weapons?     Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 6.7 thousand automatic weapons?    Answer = Round to 3 decimal places.

We will _______ if the test statistic lands in the unlikely region. Group of answer choices A. reject the alternative hypothesis B. fail to reject the null hypothesis C. cannot determine D. reject the null hypothesis and accept the alternative hypothesis

A researcher would like to predict the dependent variable YY from the two independent variables X1X1 and X2X2for a sample of N=20N=20 subjects.  Use multiple linear regression to calculate the coefficient of multiple determination and test the significance of the overall regression model.  Use a significance level α=0.02. X1X1 X2X2 YY 31.4 32.3 25.2 85.4 28.1 53 66.3 42.6 67.4 59 56.1 70.7 52.4 40.4 39.7 86.4 23.7 35 50.9 36.7 34.4 74.4 38 64.9 57.3 47.6 67.4 61.9 33.3 41.3 48.6 49.7 53.6 46.6 47.2 34.5 31.8 38.7 40.9 86 55 74 69.8 27.7 45.9 65.8 48.2 42.4 44.7 55.3 55.1 57.3 27 31.5 60.4 28.1 19.4 65.9 26 13.7 SSreg=  SSres=  R2=  F=  P-value = What is your decision for the hypothesis test? Reject the null hypothesis, H0:β1=β2=0 Fail to reject H0H0 What is your final conclusion? The evidence supports the claim that one or more of the regression coefficients is non-zero The evidence supports the claim that all of the regression…