A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additionsto savings(x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Total Coefficients Standard Error Intercept 0.0136 x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 -Write out the estimated regression equation for the relationship between the variables. (1 mark) -Compute coefficient of determination. What can you say about the strength of this relationship?  -Carry out a test to determine whether y is significantly related to the independent variables. Use a 5% level of significance. -Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.

Acrylamide is a chemical that is sometimes found in cooked starchy foods and which is thought to increase the risk of certain kinds of cancer. The paper "A Statistical Regression Model for the Estimation of Acrylamide Concentrations in French Fries for Excess Lifetime Cancer Risk Assessment"+ describes a study to investigate the effect of frying time (in seconds) and acrylamide concentration (in micrograms per kilogram) in french fries. The data in the accompanying table are approximate values read from a graph that appeared in the paper. Frying Acrylamide Time Concentration 150 240 240 270 300 300 150 125 + 195 185 135 275 USE SALT (a) Find the equation of the least-squares line for predicting acrylamide concentration using frying time. (Round your answers to four decimal places.) ŷ = (b) Does the equation of the least-squares line support the conclusion that longer frying times tend to be paired with higher acrylamide concentrations? Explain. O No, the least squares regression line…

A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a regression analysis was performed, and a portion of the computer output is as follows: ŷ = 4.5+ 14.4x Coefficients (Intercept) x Estimate 4.5 Ho: B₁ = 0 H₁: B₁ > 0 Ho: B₁ = 0 Ha: B₁ <0 14.4 Ho: B₁ = 0 Ha: B₁ #0 Std. Error Test statistic 2.9 4.7 1.55 3.06 P-value Specify the null and the alternative hypotheses that you would use in order to test whether a linear relationship exists between x and y. 0.07 0

A student used multiple regression analysis to study how family spending (y) is influenced by income (x) family size (x2), and addition to savings(x3). The variables y, x1, and x3. The variables y, x1, and x3 are measured in thousands of dollars . The following results were obtained.       ANOVA        df SS Regression 3 45.9634 Residual 11 2.6218 Total         Coefficient Standard Error Intercept 0.0136   X1 0.7992 0.074 X2 0.2280 0.190 X3 -0.5796 0.920   Write out the estimated regression equation for the relationship between the variables. Compute coefficient of determination. What can you say about the strength of this relationship? Carry out a test to determine whether y is significantly related to the independent variables. Use a 5% level of significant. Carry out a test to see if X3 and y are significantly related. Use a 5% level of significance

Consider the following computer output from a multiple regression analysis relating the cost of car insurance to the variables: number of car accidents, driver's credit score, and safety rating of the car. Intercept Car Accidents (In last 3 years) Credit Score Safety Rating Coefficients 1186 213.48 Coefficients - 130.46 294.11 Standard Error Does the sign of the coefficient for the variable safety rating make sense? 123.87 21.89 14.26 356.37 t Stat P-value 9.575 0.0000 9.752 0.0000 -9.149 0.0000 0.825 0.4128

A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings(x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained.   ANOVA                                   df                  SS Regression                3                   45.9634 Residual                  11                   2.6218 Total                                 Coefficients     Standard Error Intercept                0.0136 x1                          0.7992                   0.074 x2                          0.2280                   0.190 x3                         -0.5796                   0.920   Write out the estimated regression equation for the relationship between the variables.  Compute coefficient of determination. What can you say about the strength of this relationship?  Carry out a test to determine whether y is…

Consider the following computer output from a multiple regression analysis relating the cost of car insurance to the variables: number of car accidents, driver's credit score, and safety rating of the car. Intercept Car Accidents (In last 3 years) Credit Score Safety Rating Answer Coefficients 933 167.94 - 102.63 -199.18 Does the sign of the coefficient for the variable credit score make sense? Coefficients Standard Error 95.65 17.99 10.89 19.98 t Stat P-value 9.754 0.0000 9.335 0.0000 -9.424 0.0000 -9.969 0.0000 O Yes, because it is expected that as the credit score increases then the cost should decrease. O No, because it is expected that as the credit score increases then the cost should decrease. O Yes, because it is expected that as the credit score increases then the cost should also increase. O No, because it is expected that as the credit score increases then the cost should also increase. Tables Keypad Keyboard Shortcuts

Let's study the relationship between brand, camera resolution, and internal storage capacity on the price of smartphones. Use α = .05 to perform a regression analysis of the Smartphones01CS dataset, and then answer the following questions. When you copy and paste output from MegaStat to answer a question, remember to choose to "Keep Formatting" to paste the text. a. Did you find any evidence of multicollinearity and variance inflation among the predictors. Explain your answer using a VIF analysis. b. Copy and paste the normal probability plot for your analysis. Is there any evidence that the errors are not normally distributed? Explain. c. Copy and paste the Residuals vs. Predicted Y-values. Does the pattern support the null hypothesis of constant variance for the errors? Explain. d. Study the residuals analysis. Which observations, if any, have unusual residuals? e. Study the residuals analysis. Calculate the leverage statistic. Which observations, if any, are high leverage…

Consider the following computer output from a multiple regression analysis relating the cost of car insurance to the variables: number of car accidents, driver's credit score, and safety rating of the car. Coefficients Coefficients Standard Error t Stat P-value Intercept 956 97.23 9.832 0.0000 Car Accidents 172.08 18.24 9.434 0.0000 (In last 3 years) Credit Score Safety Rating 105.16 201.03 0.523 0.6030 -207.81 20.46 - 10.157 0.0000 Does the sign of the coefficient for the variable credit score make sense? Answer No, because it is expected that as the credit score increases then the cost should decrease. ○ No, because it is expected that as the credit score increases then the cost should also increase. ○ Yes, because it is expected that as the credit score increases then the cost should decrease. ○ Yes, because it is expected that as the credit score increases then the cost should also increase. Tables Keypad Keyboard Shortcuts