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 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.

In a multiple regression analysis involving an intercept, 15 independent variables  and 200 observations, Total SS = 800 and Residual SS = 240. Adjusted R-squared is

Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher’s salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. The Excel Regression output for the sample regression equation is given below. (a) What proportion of the variation in MCAS score is explained by the explanatory variables?    (b) At the 5% level, are the explanatory variables jointly significant in explaining MCAS score? Explain briefly.     (c) At the 5% level, which variables are individually significant at predicting MCAS score? Explain briefly.       (d) Suppose a second regression model (Model 2) was generated using only…

If a scatterplot is created in excel, and a line of regression is fit along with a derived functional form, what does it mean to describe and interpret them? What conclusions would be made about relationships between two recorded variables?