Given the linear regression model: Yi = Bo+B1x1 + ẞ2xi2 + Єi, i = 1,..., n Consider the following sums from n = 10 observations on Y, X1, and X2: 10 10 10 Σ3 = 20, Σ i=1 10 Συ? = 98.2, i=1 i=1 10 10 10 71 =0.0, Σ i=1 10 x12 = 0.0 Σαμ = 92, Σα? i=1 = 163 i=1 10 Σ Yixil = 59, Yixi2 = 88, Xi1i2=119 i=1 i=1 i=1 Explore the following steps: 1. Construct the XTX matrix and the vector XTy. 2. Calculate the least-squares estimates of Bo, B₁, and ẞ2, along with the residual sum of squares, SSE. 3. Investigate the hypothesis that the coefficient of X 2, represented by 32, is zero.

Suppose the following regression equation was generated from the sample data of 50 cities relating number of cigarette packs sold per 1000 residents in one week to tax in dollars on one pack of cigarettes and if smoking is allowed in bars: PACKS, = 59682.369232-1108.267218TAX + 176.926159BARS; + eį. BARS 1 if city i allows smoking in bars and BARS; = 0 if city i does not allow smoking in bars. This equation has an R² value of 0.347972, and the coefficient of BARS, has a P-value of 0.133971. Which of the following conclusions is valid? Answer 2 Points Keypad Keyboard Shortcuts According to the regression equation, cities that allow smoking in bars have lower cigarette sales than cities that do not allow smoking in bars. Regardless of whether or not there is a smoking ban, if a city increases its cigarette tax by one dollar cigarette sales will increase by approximately 1108 packs. ○ If there is no cigarette tax in a city that allows smoking in bars, the approximate number of cigarette…

Suppose that n = 50, i.i.d. observations for (Yi, Xi) yield the followingregression results:                      Ŷ= 49.2 + 73.9X, SER = 13.4, R2 = 0.78.                                        (23.5) (16.4)Another researcher is interested in the same regression, but makes an errorwhen entering the data into a regression program: The researcher enterseach observation twice, ending up with 100 observations (with observation1 entered twice, observation 2 entered twice and so forth).a. Using these 100 observations, what results will be produced by theregression program? (Hint: Write the “incorrect” values of the samplemeans, variances, and covariances of Y and X as functions of the “correct”values. Use these to determine the regression statistics.)           Ŷ = ____ + ____X, SER = ____, R2 = ____.                             (____) (____)b. Which (if any) of the internal validity conditions are violated?

A regression was run to determine if there is a relationship between hours of TV watched per day (x) and number of situps a person can do (y).The results of the regression were:y=ax+b a=-1.38 b=39.555 r2=0.693889 r=-0.833 Assume the correlation is significant, and use this to predict the number of situps a person who watches 7 hours of TV can do (to one decimal place)